a differential complex for cat 0 cubical spaces abstract in the 1980 s pierre julg and alain valette and also tadeusz pytlik and ryszard szwarc constructed and studied a certain fredholm operator associated to a simplicial tree the operator can be defined in at least two ways from a combinatorial flow on the tree similar to the flows in forman s discrete morse theory or from the theory of unitary operator valued cocycles there are applications of the theory surrounding the operator to c algebra k theory to the theory of completely bounded representations of groups that act on trees and to the selberg principle in the representation theory of p adic groups the main aim of this paper is to extend the constructions of julg and valette and pytlik and szwarc to cat 0 cubical spaces a secondary aim is to illustrate the utility of the extended construction by developing an application to operator k theory and giving a new proof of k amenability for groups that act properly on finite dimensional cat 0 cubical spaces

partial ordering in l underdeterminate sets abstract the purpose of this paper is to improve results on fuzzy partial orderings obtained by zadeh in 9 we overcome the difficulties connected with the axioms of antisymmetry and linearity moreover if the underlying lattice l is a complete residuated lattice we establish a szpilrajn theorem i e any l fuzzy partial ordering has a linear extension in opposition to zadeh s our point of view is that an axiom of antisymmetry without a reference to a concept of equality is meaningless therefore we first introduce the category lus cf 2 which can be considered as a mathematical model of fuzzy equality and subsequently we specify the axioms of l fuzzy partial orderings with respect to the frame given by lus the axioms we use clearly display the usefulness of having a zadeh like complementation and as a consequence the usefulness of a positivistic and nonintuitionistic frame of study an example concerning l rn which we give clearly shows that the lus version of the szpilrajn theorem cannot be reduced to a fuzzification of an already existing theorem but provides us with additional information

operator norm localization property of metric spaces under finite decomposition complexity abstract the notions of operator norm localization property and finite decomposition complexity were recently introduced in metric geometry to study the coarse novikov conjecture and the stable borel conjecture in this paper we show that a metric space x has weak finite decomposition complexity with respect to the operator norm localization property if and only if x itself has the operator norm localization property it follows that any metric space with finite decomposition complexity has the operator norm localization property in particular we obtain an alternative way to prove a very recent result by e guentner r tessera and g yu that all countable linear groups have the operator norm localization property

normal forms in bl algebra and their contribution to universal approximation of functions this paper continues the investigation of approximating properties of generalized normal forms in fuzzy logic the problem is formalized and solved algebraically normal forms are considered in two variants infinite and finite it is proved that infinite normal forms are universal representation formulas whereas finite normal forms are universal approximation formulas for any l valued function where l is a support set of any complete bl algebra the estimation of the quality of approximation is suggested moreover functions which can be precisely represented by the discrete normal forms are considered

fundamental group of simple c algebras with unique trace abstract we introduce the fundamental group f a of a unital simple c algebra a with a unique normalized trace we compute fundamental groups f a of several nuclear or non nuclear c algebras a k theoretical obstruction enables us to compute the fundamental group easily our study is essentially based on the computation of picard groups by kodaka

operator norm localization for linear groups and its application to k theory abstract we prove the operator norm localization property for linear groups as an application we prove the coarse novikov conjecture for box spaces of a linear group

the equivariant coarse novikov conjecture and coarse embedding the equivariant coarse novikov conjecture provides an algorithm for determining nonvanishing of equivariant higher index of elliptic differential operators on noncompact manifolds in this article we prove the equivariant coarse novikov conjecture under certain coarse embeddability conditions more precisely if a discrete group gamma acts on a bounded geometric space x properly isometrically and with bounded distortion x gamma and gamma admit coarse embeddings into hilbert space then the gamma equivariant coarse novikov conjecture holds for x here bounded distortion means that for any gamma in gamma sup x in y d gamma x x infty where y is a fundamental domain of the gamma action on x

higher index theory for certain expanders and gromov monster groups ii abstract in this paper the first of a series of two we continue the study of higher index theory for expanders we prove that if a sequence of graphs is an expander and the girth of the graphs tends to infinity then the coarse baum connes assembly map is injective but not surjective for the associated metric space x expanders with this girth property are a necessary ingredient in the construction of the so called gromov monster groups that coarsely contain expanders in their cayley graphs we use this connection to show that the baum connes assembly map with certain coefficients is injective but not surjective for these groups using the results of the second paper in this series we also show that the maximal baum connes assembly map with these coefficients is an isomorphism

the maximal coarse baum connes conjecture for spaces which admit a fibred coarse embedding into hilbert space abstract we introduce a notion of fibred coarse embedding into hilbert space for metric spaces which is a generalization of gromov s notion of coarse embedding into hilbert space it turns out that a large class of expander graphs admit such an embedding we show that the maximal coarse baum connes conjecture holds for metric spaces with bounded geometry which admit a fibred coarse embedding into hilbert space

interpolation by cauchy vandermonde systems and applications abstract cauchy vandermonde systems consist of rational functions with prescribed poles they are complex ect systems allowing hermite interpolation for any dimension of the basic space a survey of interpolation procedures using cv systems is given some equipped with short new proofs which generalize the well known formulas of lagrange neville aitken and newton for interpolation by algebraic polynomials the arithmetical complexitiy is o n 2 for n hermite data also inversion formulas for the cauchy vandermonde matrix are surveyed moreover a new algorithm solving the system of n linear cauchy vandermonde equations for multiple nodes and multiple poles recursively is given which does not require additional partial fraction decompositions as an application construction of rational b splines with prescribed poles is discussed

rapid decay and baum connes for large type artin groups we prove that many artin groups of large type satisfy the rapid decay property including all those of extra large type for many of these including all 3 generator groups of extra large type a result of lafforgue applies to show that the groups satisfy the baum connes conjecture without coefficients our proof of rapid decay combines elementary analysis with combinatorial techniques and relies on properties of geodesic words in artin groups of large type that were observed in earlier work by two of the authors of this current article

left and right compatibility of order relations and fuzzy tolerance relations abstract in a recent paper de baets et al have studied the compatibility of a n strict order relation with a fuzzy relation and have characterized the fuzzy tolerance and in particular fuzzy equivalence relations that a given strict order relation is compatible with we extend this study by considering the left and right compatibility of a n strict order relation with a fuzzy tolerance relation and vice versa we characterize the fuzzy tolerance relations that are compatible with a given strict order relation conversely we provide a representation of the fuzzy tolerance relations that a given strict order relation is left or right compatible with specific attention is paid to the case of fuzzy equivalence relations we conclude by pointing out that the representation theorems in the above mentioned paper need some minor rectification

k theorie bivariante pour les algebres de banach et conjecture de baum connes je suis parvenu dans ma these a construire une k theorie bivariante pour les algebres de banach cela m a permis de demontrer la conjecture de baum connes pour les groupes de lie semi simples et les groupes reductifs p adiques ainsi que pour les sous groupes discrets de type fini de sl 3 f avec f une extension finie de q p et pour les sous groupes discrets cocompacts de sp n 1 sl 3 r et sl 3 c j ai aussi demontre une conjecture analogue a la conjecture de baum connes pour les algebres l 1 et plus generalement toutes les bonnes completions des sous groupes fermes des groupes de lie semi simples et des groupes reductifs p adiques

the coarse baum connes conjecture for spaces which admit a uniform embedding into hilbert space corollary 1 2 let be a finitely generated group if as a metric space with a word length metric admits a uniform embedding into hilbert space and its classifying space b has the homotopy type of a finite cw complex then the strong novikov conjecture holds for i e the index map from k b to k c r is injective corollary 1 2 follows from theorem 1 1 and the descent principle 23 by index theory the strong novikov conjecture implies the novikov conjecture on the homotopy invariance of higher signatures cf 8 for an excellent

state space realizations of rational interpolants with prescribed poles abstract we give a generic algorithm for computing rational interpolants with prescribed poles the resulting rational function is expressed in the so called newton form state space realizations for this expression of rational functions are given our main tool for finding state space realizations is fuhrmann s shift realization theory from which we obtain concrete realizations by introducing suitable bases of the state space and expressing the abstract operators with respect to these bases in matrix form

the clone relation of a binary relation abstract in a recent paper de baets et al introduced the clone relation of a strict order relation two elements of a poset are said to be a pair of clones or to be clones if every other element that is greater resp smaller than one of them is also greater resp smaller than the other one this clone relation played a key role in the characterization of the l fuzzy tolerance relations and the l fuzzy equivalence relations that a strict order relation is compatible with in this paper we extend the notion of clone relation to any binary relation although the definition of such extension is trivial the corresponding properties significantly differ from those of the clone relation of a strict order relation we analyse the most important ones among these properties paying particular attention to a partition of the clone relation in terms of three different types of pairs of clones

the coarse novikov conjecture and banach spaces with property h in this paper we prove the coarse novikov conjecture for metric spaces with bounded geometry which are coarsely embeddable into banach spaces with a geometric condition called property h introduced by g kasparov and g yu

k theory for the maximal roe algebra of certain expanders abstract we study in this paper the maximal version of the coarse baum connes assembly map for families of expanding graphs arising from residually finite groups unlike for the usual roe algebra we show that this assembly map is closely related to the maximal baum connes assembly map for the group and is an isomorphism for a class of expanders we also introduce a quantitative baum connes assembly map and discuss its connections to k theory of maximal roe algebras

spaces of graphs boundary groupoids and the coarse baum connes conjecture we introduce a new variant of the coarse baum connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse baum connes conjecture we prove this conjecture for many coarsely disconnected spaces that are known to be counterexamples to the coarse baum connes conjecture in particular we give a geometric proof of this conjecture for spaces of graphs that have large girth and bounded vertex degree we then connect the boundary conjecture to the coarse baum connes conjecture using homological methods which allows us to exhibit all the current uniformly discrete counterexamples to the coarse baum connes conjecture in an elementary way

roe c algebra for groupoids and generalized lichnerowicz vanishing theorem for foliated manifolds we introduce the concept of roe c algebra for a locally compact groupoid whose unit space is in general not compact and that is equipped with an appropriate coarse structure and haar system using connes tangent groupoid method we introduce an analytic index for an elliptic differential operator on a lie groupoid equipped with additional metric structure which takes values in the k theory of the roe c algebra we apply our theory to derive a lichnerowicz type vanishing result for foliations on open manifolds

semigroup c algebras of ax b semigroups we study semigroup c algebras of ax b semigroups over integral domains the goal is to generalize several results about c algebras of ax b semigroups over rings of algebraic integers we prove results concerning k theory and structural properties like the ideal structure or pure infiniteness our methods allow us to treat ax b semigroups over a large class of integral domains containing all noetherian integrally closed domains and coordinate rings of affine varieties over infinite fields

non existence of non trivial l algebras containing field structure in the sense of belohlavek and an open question r email protected lohlavek has proposed the notion of l algebra in r email protected lohlavek fuzzy relational systems foundations and principles kluwer academic plenum press new york 2002 and a series of papers in this direction has been written by him and his colleague r email protected lohlavek v vychodil algebras with fuzzy equalities in proceedings of the 10th ifsa world congress june 29 july 2 2003 pp 1 4 algebras with fuzzy equalities fuzzy sets and systems accepted for publication v vychodil direct limits and reduced products of algebras with fuzzy equalities submitted for publication in this short note it will be shown that if the ordinary part of an l algebra contains two binary operations forming the field structure then the underlying l equality of the l algebra is constant trivial this means that l algebras containing field structures in their ordinary parts correspond to ordinary algebras in a one to one manner so all results in r email protected lohlavek fuzzy relational systems foundations and principles kluwer academic plenum press new york 2002 r email protected lohlavek v vychodil algebras with fuzzy equalities in proceedings of the 10th ifsa world congress june 29 july 2 2003 pp 1 4 algebras with fuzzy equalities fuzzy sets and systems accepted for publication v vychodil direct limits and reduced products of algebras with fuzzy equalities submitted for publication in their setting for l algebras containing field structure become trivial in addition to this observation other aim of this note is to draw attention to the natural question does there exist any l algebra with an l equality different from trivial l equalities in case the ordinary part of the l algebra includes two binary operations that define group ring module or vector space structure this question is equivalent to the problem of whether the notion of l algebra provides a meaningful generalization of ring module or vector space structure in the context of fuzzy equality

join completions of l ordered sets in this paper we build and characterize the join completions of an l ordered set which generalizes the join completions of a crisp poset the universal property of join completions is studied a categorical characterization of the dedekind macneille completion for an l ordered set is presented

maximal and reduced roe algebras of coarsely embeddable spaces in 7 gong wang and yu introduced a maximal or universal version of the roe c algebra associated to a metric space we study the relationship between this maximal roe algebra and the usual version in both the uniform and non uniform cases the main result is that if a uniformly discrete bounded geometry metric space x coarsely embeds into a hilbert space then the canonical map between the maximal and usual uniform roe algebras induces an isomorphism on k theory we also give a simple proof that if x has property a then the maximal and usual uniform roe algebras are the same these two results are natural coarse geometric analogues of certain well known implications of a t menability and amenability for group c algebras the techniques used are e theoretic building on work of higson kasparov and trout 11 12 and yu 28

semi invertible extensions of c algebras abstract we prolong the list of c algebras which have the property that all extensions by a stable c algebra are semi invertible in particular it is shown to include group c algebras both reduced and full of certain amalgamated free products of amenable groups as well as all free products of nuclear c algebras with amalgamation over a common nuclear c subalgebra

construction of finite l groups abstract in this paper we give some necessary and sufficient conditions for a fuzzy relation to be a compatible fuzzy equality of some l group in the sense of b lohlavek these characterizations enable practical applications for construction of l groups with a given skeleton the construction has two steps determination of the general form of fuzzy pre equalities on a group and then solving a system of inequalities in the given residuated lattice some concrete examples of construction of finite l groups with the given skeleton are presented

a theory of vague lattices based on many valued equivalence relations i general representation results the present work introduces a new and general theory of ordering relations and lattices based on many valued equivalence relations under the name vague ordering relations and vague lattices respectively representations and constructions of vague ordering relations and vague lattices are the main subjects of this paper and various desirable results in this direction are established furthermore algebraic characterizations of vague lattices are studied

operator norm localization property of relative hyperbolic group and graph of groups abstract in this article we study the spaces which have operator norm localization property we prove that a finitely generated group which is strongly hyperbolic with respect to a collection of finitely generated subgroups h 1 h n has operator norm localization property if and only if each h i i 1 2 n has operator norm localization property furthermore we prove the following result let be the fundamental group of a connected finite graph of groups with finitely generated vertex groups g p if g p has operator norm localization property for all vertices p then has operator norm localization property

metric sparsification and operator norm localization abstract we study an operator norm localization property and its applications to the coarse novikov conjecture in operator k theory in particular we introduce a sufficient geometric condition called metric sparsification for the operator norm localization property this is used to give many examples of finitely generated groups with infinite asymptotic dimension and the operator norm localization property we also show that a sequence of expanding graphs does not possess the operator norm localization property

fuzzy complete lattices in this paper based on l fuzzy posets previously introduced by the third author l fuzzy complete lattices are defined which are generalizations of usual complete lattices and coincide with wagner s complete and cocomplete w categories enriched over the frame l and are consequently a special kind of complete w lattices defined by lai and zhang however tarski fixed point theorem for the l fuzzy complete lattices is proved in a different way from that by lai and zhang furthermore some fuzzy powerset operators are suggested they are not only generalizations of ordinary powerset operators but also generalizations of l valued zadeh powerset operators and their properties are discussed

approximation of transfer functions of infinite dimensional dynamical systems by rational interpolants with prescribed poles rational interpolants with prescribed poles are used to approximate holomorphic functions on the closure of their region of analyticity under natural assumptions of their properties on the boundary the transfer functions of some infinite dimensional dynamical systems of interest in applications satisfy the restrictions we impose this is the case for discrete time fractional filters time delay systems and heat transfer control systems we give two general results by which in particular the transfer functions that arise in such dynamical systems may be approximated estimates for the rate of convergence are given we also include some numerical examples which compare the performance of the method we propose with others commonly used in systems theory

representations and constructions of similarity based fuzzy orderings this contribution advocates the dissemination of similarity based fuzzy orderings a generalized concept of fuzzy orderings which appears to be unavoidable as soon as the classical correspondences between preorderings equivalence relations and orderings are taken into account in contrast to earlier papers on the topic this paper is focused on representation and construction results which once more demonstrate the feasibility of the proposed concept

the coarse geometric novikov conjecture and uniform convexity abstract the coarse geometric novikov conjecture provides an algorithm to determine when the higher index of an elliptic operator on a noncompact space is nonzero the purpose of this paper is to prove the coarse geometric novikov conjecture for spaces which admit a coarse uniform embedding into a uniformly convex banach space

a bott periodicity theorem for infinite dimensional euclidean space abstract we formulate and prove an equivariant bott periodicity theorem for infinite dimensional euclidean vector spaces the main features of our argument are i the construction of a non commutative c algebra to play the role of the algebra of functions on infinite dimensional euclidean space and ii the construction of a certain index one elliptic partial differential operator which provides the basis for an inverse to the bott periodicity map these tools have applications to index theory and the novikov conjecture notably a proof of the novikov conjecture for amenable groups the applications will be considered elsewhere

the kadison kaplansky conjecture for word hyperbolic groups in this paper we prove the kadison kaplansky idempotent conjecture for torsion free word hyperbolic groups the conjecture asserts that the following equivalent statements hold for a torsion free discrete group the reduced group c algebra c r contains no idempotents except 0 and 1 the spectrum of every element of the reduced group c algebra is connected the canonical trace on c r takes integer values on idempotents the last assertion can be viewed as a statement about the pairing between the k theory and the local cyclic cohomology of the group c algebra it is in this setting that we will prove the conjecture our proof is based on a partial analysis of the assembly maps in k theory and local cyclic homology we compare these assembly maps by means of an equivariant bivariant chern connes character before going into details we recall some previous work on the conjecture the first progress was achieved by pimsner and voiculescu pv who proved the kadison kaplansky conjecture for free groups as a consequence of their computation of the k theory of the group c algebra subsequently it was realized that more generally the kadison kaplansky conjecture was a consequence of the baum connes conjecture which gives a geometric description of k c r for any torsion free discrete group in fact the baum connes conjecture states that the k theoretic assembly map

k theoretic amenability for sl2 qp and the action on the associated tree abstract it is proved that if a locally compact group g acts simplicially on a tree in such a way that the stabilizers of the vertices are amenable then g is k amenable in particular the canonical map from the full c algebra onto the reduced c algebra of g induces isomorphisms in k theory the main corollary of our result is that sl 2 q p and some other groups over local fields are k amenable

a clone based representation of the fuzzy tolerance or equivalence relations a strict order relation is compatible with we show that although there exists no non trivial fuzzy tolerance relation a partial order relation is compatible with in the sense of blohlvek the situation is quite different when considering its strict part more specifically we provide a representation of all fuzzy tolerance and in particular all fuzzy equivalence relations a strict order relation is compatible with to that end we introduce the notion of clone relation associated with a partially ordered set and discuss its basic properties the mentioned representation is intimately connected with this clone relation

on rigidity of roe algebras roe algebras are c algebras built using large scale or coarse aspects of a metric space x d in the special case that x is a finitely generated group and d is a word metric the simplest roe algebra associated to d is isomorphic to the crossed product c algebra l 1 r roe algebras are coarse invariants in the sense that if x and y are coarsely equivalent metric spaces then their roe algebras are isomorphic motivated in part by the coarse baum connes conjecture we ask if there is a converse to the above statement that is if x and y are metric spaces with isomorphic roe algebras must x and y be coarsely equivalent we show that for very large classes of spaces the answer to this question and some related questions is yes this can be thought of as a c rigidity result it shows that the roe algebra construction preserves a large amount of information about the space and is thus surprisingly rigid as an example of our results in the group case we have that if and are finitely generated elementary amenable hyperbolic or linear groups

the k theory of free quantum groups in this paper we study the k theory of free quantum groups in the sense of wang and van daele more precisely of free products of free unitary and free orthogonal quantum groups we show that these quantum groups are k amenable and establish an analogue of the pimsner voiculescu exact sequence as a consequence we obtain in particular an explicit computation of the k theory of free quantum groups our approach relies on a generalization of methods from the baum connes conjecture to the framework of discrete quantum groups this is based on the categorical reformulation of the baum connes conjecture developed by meyer and nest as a main result we show that free quantum groups have a gamma element and that gamma 1 as an important ingredient in the proof we adapt the dirac dual dirac method for groups acting on trees to the quantum case we use this to extend some permanence properties of the baum connes conjecture to our setting

the equivariant coarse baum connes conjecture for spaces which admit an equivariant coarse embedding into hilbert space abstract in this paper we proved that the equivariant coarse baum connes conjecture holds for a metric space with bounded geometry which admits an equivariant coarse embedding into hilbert space

approximation of delay systems a case study abstract the approximation of delay systems is studied a numerically well behaved method for computing hankel optima rational approximations for delay systems is presented based on certain properties of hankel matrices and the theory of laguerre polynomials the cf method of trefethen and certain pade approximations of delay systems are also considered the importance of a certain wiener algebra property in the analysis of the rational approximation of an important class of delay systems in the l norm and the hankel norm is shown completing certain results presented in the literature for systems satisfying certain nuclearity or absolute continuity conditions a case study and numerical comparison is presented for the approximation of the parametric family of first order stable delay systems g s exp s ts 1 numerical experience indicates that l optimized cf approximations based on short truncated maclaurin series give in general somewhat smaller l approximation errors than hankel optim

l approximation and nuclearity of delay systems abstract the l convergence of partial fraction decompositions of single input single output delay systems is studied conditions for the nuclearity of such systems are derived and examples given

higher rho invariants and the moduli space of positive scalar curvature metrics abstract given a closed smooth manifold m which carries a positive scalar curvature metric one can associate an abelian group p m to the space of positive scalar curvature metrics on this manifold the group of all diffeomorphisms of the manifold naturally acts on p m the moduli group p m of positive scalar curvature metrics is defined to be the quotient abelian group of this action i e the coinvariant of the action p m measures the size of the moduli space of positive scalar curvature metrics on m in this paper we use the higher rho invariant and the finite part of the k theory of the group c algebra of 1 m to give a lower bound of the rank of the moduli group p m the key idea of our proof is the use of higher rho invariant this is a secondary invariant associated to dirac operators and in particular depends on the choice of riemannian metric we show that the higher rho invariant remains unchanged in a certain k theory group under the action of the diffeomorphism group allowing us to distinguish elements in p m

small cancellation labellings of some infinite graphs and applications we construct small cancellation labellings for some infinite sequences of finite graphs of bounded degree we use them to define infinite graphical small cancellation presentations of groups this technique allows us to provide examples of groups with exotic properties we construct the first examples of finitely generated coarsely non amenable groups that is groups without guoliang yu s property a that are coarsely embeddable into a hilbert space moreover our groups act properly on cat 0 cubical complexes we construct the first examples of finitely generated groups with expanders embedded isometrically into their cayley graphs in contrast in the case of the gromov monster expanders are not even coarsely embedded we present further applications

euler characteristics and gysin sequences for group actions on boundaries let g be a locally compact group let x be a universal proper g space and let open image in new window be a g equivariant compactification of x that is h equivariantly contractible for each compact subgroup open image in new window let open image in new window assuming the baum connes conjecture for g with coefficients open image in new window and c x we construct an exact sequence that computes the map on k theory induced by the embedding open image in new window this exact sequence involves the equivariant euler characteristic of x which we study using an abstract notion of poincare duality in bivariant k theory as a consequence if g is torsion free and the euler characteristic open image in new window is non zero then the unit element of open image in new window is a torsion element of order open image in new window furthermore we get a new proof of a theorem of luck and rosenberg concerning the class of the de rham operator in equivariant k homology

groups acting properly on bolic spaces and the novikov conjecture we introduce a class of metric spaces which we call bolic they include hyperbolic spaces simply connected complete manifolds of nonpositive curvature euclidean buildings etc we prove the novikov conjecture on higher signatures for any discrete group which admits a proper isometric action on a bolic weakly geodesic metric space of bounded geometry

on the convergence of quadrature formulas connected with multipoint pade type approximation abstract let i f 1 1 f x x dx where is a complex valued integrable function we consider quadrature formulas for i f which are exact with respect to rational functions with prescribed poles contained in formula their rate of convergence is studied

completely lattice l ordered sets with and without l equality a relationship between l order based on an l equality and l order based on crisp equality is explored in detail this enables to clarify some properties of completely lattice l ordered sets and generalize some related assertions namely belohlavek s main theorem of fuzzy concept lattices is generalized as well as his theorem dealing with dedekind macneille completion analogously completion of an l ordered set via completely lattice l ordered set of all down l sets is described

geometrization of the strong novikov conjecture for residually finite groups in this paper we prove that the strong novikov conjecture for a residually finite group is essentially equivalent to the coarse geometric novikov conjecture for a certain metric space associated to the group as an application we obtain the coarse geometric novikov conjecture for a large class of sequences of expanders

extensions of the reduced group c algebra of a free product of amenable groups abstract we prove that the unitary equivalence classes of extensions of c r g by any unital stable c algebra taken modulo extensions which split via an asymptotic homomorphism form a group which can be calculated from the universal coefficient theorem of kk theory when g is a free product of a countable collection of countable amenable groups

an answer to demirci s open question a clarification of his result and a correction of his interpretation of the result in his note this issue of this journal demirci shows that fields with fuzzy equalities have only trivial fuzzy equalities concludes that therefore in case l algebras contain field structure all results in r belohlavek fuzzy relational systems foundations and principles kluwer academic plenum publishers new york 2002 r belohlavek v vychodil algebras with fuzzy equalities in proceedings of the 10th ifsa world congress june 29 july 2 2003 pp 1 4 r belohlavek v vychodil algebras with fuzzy equalities fuzzy sets and systems accepted v vychodil direct limits and reduced products of algebras with fuzzy eqalities submitted are evident from their classical counterparts and asks a question does there exist any l algebra with an l equality different from trivial l equalities in case the ordinary part of the l algebra includes two binary operations that define group ring module or vector space structure in our reply we show the following first by presenting examples of group based l algebras with non trivial l equalities we show that the answer to demirci s question is positive second we clarify the meaning of demirci s result and show that it is in fact a natural generalization of the well known classical result saying that ordinary fields do not have non trivial congruences third we argue that demirci s interpretation of his result is mistaken and that it is not true that all results in r belohlavek fuzzy relational systems foundations and principles kluwer academic plenum publishers new york 2002 r belohlavek v vychodil algebras with fuzzy equalities fuzzy sets and systems to appear r belohlavek v vychodil fuzzy equational logic springer berlin to appear s burris h p sankappanavar a course in universal algebra springer new york 1981 are evident from their classical counterparts

quantitative k theory and the kunneth formula for operator algebras abstract in this paper we apply quantitative operator k theory to develop an algorithm for computing k theory for the class of filtered c algebras with asymptotic finite nuclear decomposition as a consequence we prove the kunneth formula for c algebras in this class our main technical tool is a quantitative mayer vietoris sequence for k theory of filtered c algebras

e theory and kk theory for groups which act properly and isometrically on hilbert space a good deal of research in c algebra k theory in recent years has been devoted to the baum connes conjecture 3 which proposes a formula for the k theory of group c algebras that blends group homology with the representation theory of compact subgroups the conjecture has brought c algebra theory into close contact with manifold theory through its obvious similarity to the borel conjecture of surgery theory 9 31 and its links with the theory of positive scalar curvature 27 in addition there are points of contact with harmonic analysis particularly the tempered representation theory of semisimple groups although the proper relation between the baum connes conjecture and representation theory is not well understood the conjecture is most easily formulated for groups which are discrete and torsion free for such a group g there is a natural homomorphism

exotic crossed products and the baum connes conjecture we study general properties of exotic crossed product functors and characterise those which extend to functors on equivariant c algebra categories based on correspondences we show that every such functor allows the construction of a descent in kk theory and we use this to show that all crossed products by correspondence functors of k amenable groups are kk equivalent we also show that for second countable groups the minimal exact morita compatible crossed product functor used in the new formulation of the baum connes conjecture by baum guentner and willett 4 extends to correspondences when restricted to separable g c algebras it therefore allows a descent in kk theory for separable systems

fibred coarse embedding into non positively curved manifolds and higher index problem abstract let x n 1 x n be the coarse disjoint union of a sequence of finite metric spaces with uniform bounded geometry in this paper we show that the coarse novikov conjecture holds for x if x admits a fibred coarse embedding into a simply connected complete riemannian manifold of non positive sectional curvature this includes a large class of expander graphs with geometric property t

the novikov conjecture for groups with finite asymptotic dimension recall that the asymptotic dimension is a coarse geometric analogue of the covering dimension in topology page 28 14 more precisely the asymptotic dimension for a metric space is the smallest integer n such that for any r 0 there exists a uniformly bounded cover c ui iei of the metric space for which the r multiplicity of c is at most n 1 i e no ball of radius r in the metric space intersects more than n 1 members of c 14 the class of finitely generated discrete groups with finite asymptotic dimension is hereditary in the sense that if a finitely generated group has finite asymptotic dimension as metric space with a word length metric then its finitely generated subgroups also have finite asymptotic dimension as metric spaces with word length metrics cf section 6 this together with a result of gromov in 14 implies that finitely generated subgroups of gromov s hyperbolic groups have finite asymptotic dimension currently no example of a finitely generated group with infinite asymptotic dimension and finite classifying space is known it should also be noted that two different definitions of asymptotic dimension

the stability of local properties of fuzzy relations under ordinal equivalence abstract we consider a notion of equivalence relation between fuzzy relations and its properties the relation is called ordinal equivalence since it partitions the family of fuzzy relations into equivalence classes by means of the order defined on elements of each relation we compare fuzzy relations by their membership values and as a consequence we propose two types of local properties of fuzzy relations new properties of fuzzy relations are more compatible with the ordinal equivalence relation namely they are stable in the equivalence classes moreover we study dependencies between these new properties of fuzzy relations finally notes on applications of the presented local properties and the ordinal equivalence relation are provided