crossed products of c correspondences by amenable group actions abstract let x a be a c correspondence with a continuous action by an amenable locally compact group g we will show that if x g a g is the induced c correspondence and is the induced action on o x then o x g o x g as applications we obtain b abadie takai duality for crossed products by hilbert c modules preprint arxiv 0709 1122v1 proposition 4 5 and a kumjian d pask c algebras of directed graphs and group actions ergodic theory dynam systems 19 6 1999 1503 1519 corollary 2 5

a class of methods based on non polynomial sextic spline functions for the solution of a special fifth order boundary value problems a family of fourth and second order accurate numerical schemes is presented for the solution of fifth order boundary value problems with two point boundary conditions the non polynomial sextic spline functions are applied to construct the numerical algorithms this approach generalizes polynomial spline algorithms and provides solution at every point of range of integration convergence of the methods is discussed through standard convergence analysis a numerical illustration is given to show the pertinent features of the technique

equivariant novikov conjecture for groups acting on euclidean buildings we prove the equivariant novikov conjecture for groups acting on euclidean buildings by using an equivariant f tilsum skandalis methocl we also obtain an equivariant version of the connes gromov moscovic th eorem for almost flat c algebra bundles

localizing gauge theories from noncommutative geometry abstract we recall the emergence within noncommutative geometry of a generalized gauge theory from a real spectral triple for a unital c algebra a this includes a gauge group determined by the unitaries in a and gauge fields arising from a so called perturbation semigroup which is associated to a our main new result is the construction of an upper semi continuous c bundle on a hausdorff base space x whose space of continuous sections is isomorphic to a the gauge group acts by vertical automorphisms on this c bundle and can under some conditions be identified with the space of continuous sections of a group bundle on x moreover in some cases the gauge group is found to coincide with the group of inner automorphisms of a we discuss two classes of examples of our construction yang mills theory and toric noncommutative manifolds and we show that they actually give rise to continuous c bundles moreover in these examples the gauge groups coincide with the inner automorphism groups and can be realized as spaces of sections of group bundles that we explicitly determine

quartic non polynomial spline approach to the solution of a system of third order boundary value problems quartic non polynomial splines are used to develop a new numerical method for computing approximations to the solution of a system of third order boundary value problems associated with obstacle unilateral and contact problems it is shown that the new method gives approximations which are better than those produced by other collocation finite difference and spline methods convergence analysis of the method is discussed through standard procedures a numerical example is given to illustrate the applicability and efficiency of the novel method

on the asymptotic stability for nonautonomous functional differential equations by lyapunov functionals sufficient conditions are given for the asymptotic stability and uniform asymptotic stability of the zero solution of the nonautonomous fde s whose right hand sides can be unbounded functions of the time the theorems are based upon lyapunov krasovskii functionals whose derivatives with respect to the equations are negative semidefinite and can vanish at long intervals the functionals and their derivatives are estimated by either x t the norm of the instantaneous value of the solutions or x t 2 the l 2 norm of the phase segment of the solutions examples are given to show that the conditions are sharp and the main theorems with the two different types of estimates are independent and improve earlier results the theorems are applied to linear and nonlinear retarded fde s with one delay and with distributed delays

solving third order obstacle problems with quartic b splines in this paper we develop a new numerical method for solving a system of third order boundary value problems associated with third order obstacle problems using the quartic b splines the convergence order of the method is considered and numerical results are also given

the c algebra of a vector bundle and fields of cuntz algebras abstract we study the cuntz pimsner algebra associated with the module of continuous sections of a hilbert bundle and prove that it is a continuous bundle of cuntz algebras furthermore we assign to bundles of cuntz algebras carrying a global circle action a class in the representable kk group of the zero grade bundle we explicitly compute such class for the cuntz pimsner algebra of a vector bundle

controlled k theory for groupoids applications to coarse geometry abstract we develop a generalization of quantitative k theory which we call controlled k theory it is powerful enough to study the k theory of crossed product of c algebras by action of etale groupoids and discrete quantum groups in this article we will use it to study groupoids crossed products we define controlled assembly maps which factorize the baum connes assembly maps and define the controlled baum connes conjecture we relate the controlled conjecture for groupoids to the classical conjecture and to the coarse baum connes conjecture this allows to give applications to coarse geometry in particular we can prove that the maximal version of the controlled coarse baum connes conjecture is satisfied for a coarse space which admits a fibred coarse embedding which is a stronger version of a result of m finn sell

cubic splines method for a system of third order boundary value problems we use uniform cubic polynomial splines to develop a numerical method for computing approximations to the solution of a system of third order boundary value problem associated with odd order obstacle problems such problems arise in physical oceanography and can be studied in the framework of variational inequality theory the convergence analysis of the new method is studied and an upper bound for the error is derived a numerical example is given to illustrate the efficiency of the new method

algebraic k theory of stable c algebras abstract let a be a unital c algebra and let l denote the calkin algebra the bounded operators on a separable hilbert space modulo the compact operators k we prove the following conjecture of m karoubi the algebraic and topological k theory groups of the tensor product c algebra a l are equal the algebra a l may be regarded as a suspension of the more elementary c algebra a k thus karoubi s conjecture asserts roughly speaking that the algebraic and topological k theories of stable c algebras agree

the ring structure for equivariant twisted k theory we prove under some mild conditions that the equivariant twisted k theory group of a crossed module admits a ring structure if the twisting 2 cocycle is 2multiplicative we also give an explicit construction of the transgression map t1 h a h 1 n o a for any crossed module n and prove that any element in the image is multiplicative as a consequence we prove that under some mild conditions for a crossed module n and any e s that the equivariant twisted k theory group k e n admits a ring structure as an application we prove that for a compact connected and simply connected lie group g the equivariant twisted k theory group k c g g is endowed with a canonical ring structurek c g g k j d c g g k i j d c g g where d dimg and c h gog s

on the stability of solutions of certain fourth order delay differential equations the paper gives sufficient conditions for the asymptotic stability of the zero solutions of systems 1 and 2 by constructing lyapunov functionals we obtained the results in a very simple form

groupoids and an index theorem for conical pseudo manifolds we define an analytical index map and a topological index map for conical pseudomanifolds these constructions generalize the analogous constructions used by atiyah and singer in the proof of their topological index theorem for a smooth compact manifold m a main ingredient is a non commutative algebra that plays in our setting the role of c 0 t m we prove a thom isomorphism between non commutative algebras which gives a new example of wrong way functoriality in k theory we then give a new proof of the atiyah singer index theorem using deformation groupoids and show how it generalizes to conical pseudomanifolds we thus prove a topological index theorem for conical pseudomanifolds

the c0 x algebra of a net and index theory abstract given a connected and locally compact hausdorff space x with a good base k we assign in a functorial way a c 0 x algebra to any precosheaf of c algebras a defined over k afterwards we consider the representation theory and the kasparov k homology of a and interpret them in terms respectively of the representation theory and the k homology of the associated c 0 x algebra when a is an observable net over the spacetime x in the sense of algebraic quantum field theory this yields a geometric description of the recently discovered representations affected by the topology of x

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

mathcal c _ 0 x algebras stability and strongly self absorbing mathcal c algebras we study permanence properties of the classes of stable and so called mathcal d stable mathcal c algebras respectively more precisely we show that a mathcal c 0 x algebra a is stable if all its fibres are provided that the underlying compact metrizable space x has finite covering dimension or that the cuntz semigroup of a is almost unperforated a condition which is automatically satisfied for mathcal c algebras absorbing the jiang su algebra mathcal z tensorially furthermore we prove that if mathcal d is a k 1 injective strongly self absorbing mathcal c algebra then a absorbs mathcal d tensorially if and only if all its fibres do again provided that x is finite dimensional this latter statement generalizes results of blanchard and kirchberg we also show that the condition on the dimension of x cannot be dropped along the way we obtain a useful characterization of when a mathcal c algebra with weakly unperforated cuntz semigroup is stable which allows us to show that stability passes to extensions of mathcal z absorbing mathcal c algebras

rokhlin dimension for flows we introduce a notion of rokhlin dimension for one parameter automorphism groups of c algebras this generalizes kishimoto s rokhlin property for flows and is analogous to the notion of rokhlin dimension for actions of the integers and other discrete groups introduced by the authors and zacharias in previous papers we show that finite nuclear dimension and absorption of a strongly self absorbing c algebra are preserved under forming crossed products by flows with finite rokhlin dimension and that these crossed products are stable furthermore we show that a flow on a commutative c algebra arising from a free topological flow has finite rokhlin dimension whenever the spectrum is a locally compact metrizable space with finite covering dimension for flows that are both free and minimal this has strong consequences for the associated crossed product c algebras those containing a non zero projection are classified by the elliott invariant for compact manifolds this consists of topological k theory together with the space of invariant probability measures and a natural pairing given by the ruelle sullivan map

non polynomial spline approach to the solution of a system of third order boundary value problems we use a quartic spline equivalent nonpolynomial spline functions to develop a numerical method for computing approximations to the solution of a system of third order boundary value problems associated with obstacle unilateral and contact problems we show that the present method gives approximations which are better than those produced by other collocation finite difference and spline methods a numerical example is given to illustrate the applicability and efficiency of the new method

la k theorie de la c algebre pleine de sl3 c abstract let g be sl 3 c c g c r g the morphism induced by the regular representation and e c g c the trivial representation we prove that e induces a kk equivalence between c g and c r g c we prove this by comparing c g with c g p g where p is a maximal parabolic subgroup in g as a corollary we obtain the computation of k c g

some remarks on kasparov theory on considere une autre preuve de l invariance d homotopie du bifoncteur ext on etudie l associativite du produit de kasparov a travers la motion de connextion

one more pathology of c algebraic tensor products we define a collection of tensor product norms for c algebras and show that a symmetric tensor product functor on the category of separable c algebras need not be associative

the generator problem for z stable c algebras the generator problem was posed by kadison in 1967 and it remains open until today we provide a solution for the class of c algebras absorbing the jiang su algebra z tensorially more precisely we show that every unital separable z stable c algebra a is singly generated which means that there exists an element x a that is not contained in any proper sub c algebra of a to give applications of our result we observe that z can be embedded into the reduced group c algebra of a discrete group that contains a non cyclic free subgroup it follows that certain tensor products with reduced group c algebras are singly generated in particular c r f c r f is singly generated

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

smooth dense subalgebras of reduced group c algebras schwartz cohomology of groups and cyclic cohomology abstract we introduce the notion of schwartz co homology of a discrete group with a length function which is the natural generalization of the bounded cohomology of a discrete group we prove that if the length function is chosen to be a word length on a group of polynomial growth then its schwartz cohomology is canonically isomorphic to the usual group cohomology with complex coefficients using this result we will show that the group cohomology of a discrete group of polynomial growth is of polynomial growth in the sense of connes and moscovici and that there are no nontrivial idempotents in the group c algebra of a torsion free group of polynomial growth by the method of cyclic cohomology of connes

all extensions of c _r left mathbb f_n right are semi invertible it is shown that an extension of the reduced group c algebra of a free group by the compact operators can be made asymptotically split by addition of another extension which admits a completely positive lifting

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

nonpolynomial spline approach to the solution of a system of second order boundary value problems we use a cubic spline equivalent nonpolynomial spline functions to develop a numerical method for computing approximations to the solution of a system of second order boundary value problems associated with obstacle unilateral and contact problems we show that the present method gives approximations which are better than those produced by other collocation finite difference and spline methods convergence analysis of the method is discussed a numerical example is given to illustrate practical usefulness of our method

equivariant lefschetz maps for simplicial complexes and smooth manifolds let x be a locally compact space with a continuous proper action of a locally compact group g assuming that x satisfies a certain kind of duality in equivariant bivariant kasparov theory we can enrich the classical construction of lefschetz numbers for self maps to an equivariant k homology class we compute the lefschetz invariants for self maps of finite dimensional simplicial complexes and smooth manifolds the resulting invariants are independent of the extra structure used to compute them since smooth manifolds can be triangulated we get two formulas for the same lefschetz invariant in this case the resulting identity is closely related to the equivariant lefschetz fixed point theorem of luck and rosenberg

on the k theory of groups with finite asymptotic dimension it is proved that the assembly maps in algebraic kand l theory with respect to the family of finite subgroups is injective for groups with finite asymptotic dimension that admit a finite model for e the result also applies to certain groups that admit only a finite dimensional model for e in particular it applies to discrete subgroups of virtually connected lie groups

on the relation between k and l theory of c algebras we prove the existence of a map of spectra tau a ka rightarrow ell a between connective topological k theory and connective algebraic l theory of a complex c algebra a which is natural in a and compatible with multiplicative structures we determine its effect on homotopy groups and as a consequence obtain a natural equivalence ka left tfrac 1 2 right xrightarrow simeq la left tfrac 1 2 right of periodic k and l theory spectra after inverting 2 we show that this equivalence extends to k and l theory of real c algebras using this we give a comparison between the real baum connes conjecture and the l theoretic farrell jones conjecture we conclude that these conjectures are equivalent after inverting 2 if and only if a certain completion conjecture in l theory is true

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

the baum connes conjecture for free orthogonal quantum groups we prove an analogue of the baum connes conjecture for free orthogonal quantum groups more precisely we show that these quantum groups have a element and that 1 it follows that free orthogonal quantum groups are k amenable we compute explicitly their k theory and deduce in the unimodular case that the corresponding reduced c algebras do not contain nontrivial idempotents our approach is based on the reformulation of the baum connes conjecture by meyer and nest using the language of triangulated categories an important ingredient is the theory of monoidal equivalence of compact quantum groups developed by bichon de rijdt and vaes this allows us to study the problem in terms of the quantum group suq 2 the crucial part of the argument is a detailed analysis of the equivariant kasparov theory of the standard podle

realizing the analytic surgery group of higson and roe geometrically part iii higher invariants we construct an isomorphism between the geometric model and higson roe s analytic surgery group reconciling the constructions in the previous papers in the series on realizing the analytic surgery group of higson and roe geometrically with their analytic counterparts following work of lott and wahl we construct a chern character on the geometric model for the surgery group it is a delocalized chern character from which lott s higher delocalized rho invariants can be retrieved following work of piazza and schick we construct a geometric map from stolz positive scalar curvature sequence to the geometric model of higson roe s analytic surgery exact sequence

quartic splines solutions of third order obstacle problems in this paper we develop a new numerical method for solving a system of third order boundary value problems associated with third order obstacle problems using the quartic splines its convergence analysis is also considered to illustrate its efficiency we give an example which shows that this method gives better results

a class of methods based on non polynomial spline functions for the solution of a special fourth order boundary value problems with engineering applications we use a quintic non polynomial spline functions to develop a numerical method for computing approximations to the solution of a system of fourth order boundary value problems associated with plate deflection theory we show that the present family of methods gives better approximations and generalize all the existing finite difference and spline functions based methods up to order six convergence of the methods is shown through standard convergence analysis numerical exampls are given to illustrate the applicability and efficiency of the new method

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

approximate computation of eigenvalues with chebyshev collocation method in this study chebyshev collocation method is investigated for the approximate computation of higher sturm liouville eigenvalues by a truncated chebyshev series using the chebyshev collocation points this method transform the sturm liouville problems and given boundary conditions to matrix equation by solving the algebraic equation system the approximate eigenvalues can be computed hence by using asymptotic correction technique corrected eigenvalues can be obtained

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

continuous fields of c algebras arising from extensions of tensor c categories abstract the notion of extension of a given c category c by a c algebra a is introduced in the commutative case a c the objects of the extension category are interpreted as fiber bundles over of objects belonging to the initial category it is shown that the doplicher roberts algebra dr algebra in the following associated to an object in the extension of a strict tensor c category is a continuous field of dr algebras coming from the initial one in the case of the category of the hermitian vector bundles over the general result implies that the dr algebra of a vector bundle is a continuous field of cuntz algebras some applications to pimsner c algebras are given

on the stability and boundedness of solutions of a kind of third order delay differential equations abstract in this paper we study eq 1 1 for asymptotic stability of the zero solution when p t x x x 0 and uniformly bounded and uniformly ultimate bounded of all solutions when p t x x x 0

equivariant comparison of quantum homogeneous spaces we consider the quantum homogeneous spaces of the q deformation of simply connected simple compact lie groups and their poisson lie quantum subgroups we prove the deformation invariance in the equivariant kk theory with respect to the translation action by maximal tori this extends a result of neshveyev and tuset to the equivariant setting as applications we prove the ring isomorphism of the k homology of gq with respect to the coproduct of c gq and an analogue of the borsuk ulam theorem for quantum spheres

poincare duality for cuntz pimsner algebras abstract we present a new approach to poincare duality for cuntz pimsner algebras we provide sufficient conditions under which poincare self duality for the coefficient algebra of a hilbert bimodule lifts to poincare self duality for the associated cuntz pimsner algebra with these conditions in hand we can constructively produce fundamental classes in k theory for a wide range of examples we can also produce k homology fundamental classes for the important examples of cuntz krieger algebras following kaminker putnam and crossed products of manifolds by isometries and their non commutative analogues

identifying assembly maps in k and l theory in this paper we prove the equivalence of various algebraically or geometrically defined assembly maps used in formulating the main conjectures in k and l theory and c theory

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