the approximate tubular neighborhood theorem skeleta and other pure subsets of manifold stratified spaces are shown to have neighborhoods which are teardrops of stratified approximate fibrations under dimension and compactness assumptions in general the stratified approximate fibrations cannot be replaced by bundles and the teardrops cannot be replaced by mapping cylinder neighborhoods thus this is the best possible topological tubular neighborhood theorem in the stratified setting

the poisson boundary of teichmuller space abstract for a markov operator on teichmuller space commuting with the action of the mapping class group we prove convergence of sample paths of the associated markov chain in the thurston compactification and show that the poisson boundary of the markov operator can be identified with the space of projective measured foliations the approach consists in using the authors results on the poisson boundary of the mapping class group in combination with a discretization procedure based on a harnack inequality for markov operators on teichmuller space

rigidity of coxeter groups let w be a coxeter group acting properly discontinuously and cocompactly on manifolds n and m 9m 0 such that the fixed point sets of finite subgroups are contractible let f n n mx dk m xsk1 be a w homotopy equivalence which restricts to a w homeomorphism on the boundary under an assumption on the three dimensional fixed point sets we show that then f is w homotopic to a w homeomorphism

ends of maps ii versions of the finiteness obstruction and simple homotopy theory within e overx are developed this provides a setting for obstructions to the map analogs of the end ands cobordism theorems for manifolds these are applied to study equivariant mapping cylinder neighborhoods in topological group actions triangulations of locally triangulable spaces and block bundle structures on approximate fibrations

the periodicity in stable equivariant surgery the classical surgery theory see 5 and 23 computes the structure set sm m rel of manifolds homotopy equivalent to m relative to the boundary siebenmann showed that in topological category the structure set is 4 periodic sm m rel sm 4 m d4 rel up to a copy of see 12 cappell and weinberger gave a geometric interpretation of this periodicity in 8 by using weinberger s stratified surgery theory see 24 we extend this to an equivariant periodicity result for topological manifolds with homotopically stratified actions by compact lie groups with d4 replaced by the unit ball of certain group representations in particular if g is an odd order group acting on a topological manifold m then the equivariant stable structure sets satisfy s m rel s m d 4 g rel up to copies of 1993 john wiley sons inc

stratified path spaces and fibrations the main objects of study are the homotopically stratified metric spaces introduced by quinn closed unions of strata are shown to be stratified forward tame stratified fibrations between spaces with stratifications are introduced paths which lie in a single stratum except possibly at their initial points form a space with a natural stratification and the evaluation map from that space of paths is shown to be a stratified fibration applications to mapping cylinders and to the geometry of manifold stratified spaces are expected in future papers

positive harmonic functions on complete manifolds of negative curvature this paper studies the interaction between the geometry of complete riemannian manifolds of negative curvature and some aspects of function theory on these spaces the study of harmonic functions on the unit disc provides a classical and beautiful example of this interaction we recall some aspects of this below there is a well known representation of positive harmonic functions on the unit disc u due to herglotz 13 in terms of positive borel measures tt on the circle s1

the dirichlet problem at infinity for random walks on graphs with a strong isoperimetric inequality we study the spatial behaviour of random walks on infinite graphs which are not necessarily invariant under some transitive group action and whose transition probabilities may have infinite range we assume that the underlying graphg satisfies a strong isoperimetric inequality and that the transition operatorp is strongly reversible uniformly irreducible and satisfies a uniform first moment condition we prove that under these hypotheses the random walk converges almost surely to a random end ofg and that the dirichlet problem forp harmonic functions is solvable with respect to the end compactification if in addition the graph as a metric space is hyperbolic in the sense of gromov then the same conclusions also hold for the hyperbolic compactification in the place of the end compactification the main tool is the exponential decay of the transition probabilities implied by the strong isoperimetric inequality finally it is shown how the same technique can be applied to brownian motion to obtain analogous results for riemannian manifolds satisfying cheeger s isoperimetric inequality in particular in this general context new and simpler proofs of well known results on the dirichlet problem for negatively curved manifolds are obtained

nonlinear similarity begins in dimension six the real representations pi and p2 of a finite group g are topologically similar written pi t p2 if there is a homeomorphism h v p1 v pa where v pi denotes the vector space of the representation pi such that h p1 g v p2 g h v for v e v p1 and g e g i e the representation spaces are equivariantly homeomorphic de rham dr conjectured that topological similarity implies the linear equivalence of the two representations the first two authors showed that de rham s conjecture is true for representations of dimension less than six cs6 but false for representations of dimension greater than or equal to nine cs2 here we give examples of nonlinear similarity i e topological similarity between linearly inequivalent representations in dimension six which is therefore the minimal dimension in which nonlinear similarity may occur since linear equivalence is detected by cyclic subgroups a minimal counterexample to de rham s conjecture will occur for g cyclic moreover by hp and mr nonlinear similarity may only occur for groups whose order is divisible by four thus we shall restrict attention to g z4q the cyclic group of order 4q we shall construct six dimensional nonlinear similarities of z4q for every q greater than two moreover we shall show in a later paper cssww2 joint with weinberger that the examples here represent all six dimensional nonlinear similarities of cyclic groups actually we shall give the complete topological classification of representations of the form p 6 c where p is free i e z4q acts freely away from the origin in the representation space of p and 6 and e are the nontrivial and trivial one dimensional representations respectively representations of the form p 6 were studied in cs2 suppose that pi 6 c 1t p2 6 e with p1 and p2 free let lp be the orbit space of the unit

constructing approximate fibrations in this paper two results concerning the construction of approximate fibrations are established the first shows that there are approximate fibrations p m s2 which are homotopic to bundle maps but which cannot be approximated by bundle maps here m can be a compact q manifold or some topological n manifold n 5 the second shows how to construct approximate fibrations p m b whose fibers do not have finite homotopy type for any b of euler characteristic zero here m can be a compact q manifold and b only has to be an anr or m can be an n manifold n 6 and b must then also be a topological manifold

parallel equalization structure for mimo fbmc oqam systems under strong time and frequency selectivity offset qam based filterbank multicarrier fbmc oqam has been shown to be a promising alternative to cyclic prefix orthogonal frequency division multiplexing for the future generation of wireless communication systems unfortunately as the channel gets more selective in time and frequency the fbmc oqam orthogonality is progressively destroyed and distortion appears after the demodulation process at the receiver while channel frequency selectivity has been very widely studied in the fbmc literature the impact of time selectivity of the channel has not received that much attention in this paper the effect of the two types of selectivity on a multiple input multiple output mimo fbmc system is characterized and a parallel equalization structure that can compensate for the doubly dispersive nature of the channel is proposed this design uses multiple analysis filterbanks and extends previous approaches that were dealing only with channel frequency selectivity a theoretical approximation of the remaining distortion after equalization is given the study is performed for a general mimo system but can also be particularized to single input single output systems simulation results demonstrate the high efficiency of the proposed receiver structure and the accuracy of the theoretical approximations is verified

negatively curved manifolds elliptic operators and the martin boundary consider a riemannian manifold m of dimension n 2 and assume that m is complete simply connected and that its sectional curvatures are bounded between two negative constants in a recent paper 7 m anderson and r schoen have proved that the martin boundary of m with respect to the laplace beltrami operator a is naturally homeomorphic to soo m the sphere at infinity of m here we shall first establish a similar result for a wide class of elliptic operators on m giving at the same time a new proof of the theorem of anderson and schoen our proof relies heavily on several concepts of potential theory but on the other hand avoids the quite difficult calculations of 7 and perhaps makes the result more understandable roughly speaking we show that if y is a second order elliptic operator defined over m and has a uniformly nice behaviour on each ball of radius 1 in m then dq m the y martin boundary of m is s m provided that the following condition holds there is a positive y ci superharmonic function on m for some positive if instead we only assume the existence of the green function for y a minimal requirement when studying the y martin boundary then d m may be very different from so m even for a rotation invariant operator y on the unit ball of rn equipped

the k theoretic farrell jones conjecture for hyperbolic groups we prove the k theoretic farrell jones conjecture for hyperbolic groups with twisted coefficients in any associative ring with unit

on the k theory of crystallographic groups for any crystallographic group f we show that the groups ki t are isomorphic via the forget control map to the controlled a groups ki r c for all 0

rigidity and crystallographic groups i this is the first in a series of articles about rigidity theorems for crystallographic groups the main theorem is 1 1 it is an h cobordism rigidity statement it implies see 1 6 that any crystallographic manifold with odd order holonomy which is h cobordant and simply homotopically equivalent to the standard one is actually homeomorphic to it in the second part of this work 9 we will exploit this result to prove that one can remove the word h cobordant from the previous sentence the main theorem concerns an involution on the group wh p mr this is the group of g h cobordisms of the flat torus mr of a crystallographic group f with holonomy group g definitions of these terms appear in 1 4 we prove a vanishing result of the tate cohomology

the dirichlet problem at infinity for a negatively curved manifold on considere une n variete de riemann complete m qui est connexe et simplement connexe et a des courbures sectionnelles k bornees par 2 constantes finies negatives on etudie l existence de fonctions harmoniques bornees non constantes pour ces varietes

analysis and design of ofdm oqam systems based on filterbank theory a discrete time analysis of the orthogonal frequency division multiplex offset qam ofdm oqam multicarrier modulation technique leading to a modulated transmultiplexer is presented the conditions of discrete orthogonality are established with respect to the polyphase components of the ofdm oqam prototype filter which is assumed to be symmetrical and with arbitrary length fast implementation schemes of the ofdm oqam modulator and demodulator are provided which are based on the inverse fast fourier transform non orthogonal prototypes create intersymbol and interchannel interferences isi and ici that in the case of a distortion free transmission are expressed by a closed form expression a large set of design examples is presented for ofdm oqam systems with the number of subcarriers going from four up to 2048 which also allows a comparison between different approaches to get well localized prototypes

approximation by equivariant homeomorphisms i locally linear locally smoothable actions of finite groups on finite dimensional manifolds are considered in which two incident components of fixed point sets of subgroups either coincide or one has codimension at least three in the other for these actions an equivariant o approximation theorem is proved using engulfing techniques as corollaries are obtained equivariant fibrations are bundles and controlled h cobordism theorems as well as an equivariant version of edwards cell like mapping theorem and the vanishing of the set of transfer invariant g homotopy topological structures rel bound ary on tn x dp when tn is the n torus with trivial g action and dp is a representation disc here we consider locally linear locally smooth br pl and topological actions of a finite group g on n manifolds in addition we require that a g manifold m have gaps of codimension 3 i e for h c g if mh is a component of the h fixed point set mh and m h c mh is the subspace of points x for which the isotropy subgroup gx strictly contains h then either m h mh or m h has codimension 3 in mh we shall use the term not necessarily locally linear g manifold when we wish to drop the local linearity hypothesis but retain the property that if mh c m but mh m then mh is a locally flat inequivariantly submanifold of mk of codimension at least three this while self contained is the second in a series of papers sw2 8 s in which we analyze the extent of failure of the topological invariance of equivari ant whitehead torsion and the consequent failure of subgroups of the equivariant whitehead group whgl m of illman ill cf rothenberg r to classify pl or smooth g h cobordisms up to topological equivalence under our gap hypotheses the arguments of browder and quinn bq and rothenberg r show that g h cobordisms are classified up to pl or smooth equivalence by such subgroups we eventually conclude in sw7 s cf sw2 that the topological equivalence classes of g h cobordisms on a g manifold m that are products over the union of fixed point components of m having dimension 5 are classised by a group whg p m to which whgl m maps homomorphically the image in whg p m of the per tinent subgroup of whgl m classifies up to equivariant homeomorphism rel m those g h cobordisms on m that admit equivariant handlebody decompositions relative to m this homomorphism is not generally surjective and there are g h cobordisms that do not admit such handle decompositions cf sw5 s in order

stratified fiber bundles quinn homology and brane stability of hyperbolic orbifolds we revisit the problem of stability of string vacua involving hyperbolic orbifolds using methods from homotopy theory and k homology we propose a definition of type ii string theory on such backgrounds that further carry stratified systems of fiber bundles which generalize the more conventional orbifold and symmetric string backgrounds together with a classification of wrapped branes by a suitable generalized homology theory for spaces stratified fibered over hyperbolic orbifolds we use the algebraic k theory of their fundamental groups and quinn homology to derive criteria for brane stability in terms of an atiyah hirzebruch type spectral sequence with its lift to k homology stable d branes in this setting carry stratified charges which induce new additive structures on the corresponding k homology groups we extend these considerations to backgrounds which support h flux where we use k groups of twisted group algebras of the fundamental groups to analyze stability of locally symmetric spaces with k amenable isometry groups and derive stability conditions for branes wrapping the fibers of an eilenberg maclane spectrum functor

the farrell jones isomorphism conjecture for finite covolume hyperbolic actions and the algebraic theory of bianchi groups we prove the farrell jones isomorphism conjecture for groups acting properly discontinuously via isometries on real hyperbolic n space ihin with finite volume orbit space we then apply this result to show that for any bianchi group f wh f ko zr and ki zr vanish for i 1

an end theorem for stratified spaces we show that a manifold stratified space x is the interior of a compact manifold stratified space with boundary if and only if x is tame ended and a k theoretic obstruction x vanishes the obstruction x is a localization of quinn s mapping cylinder neighborhood obstruction the main results are theorem 1 6 and theorem 1 7 below in particular this explains when a g manifold is the interior of a compact g manifold with boundary one of our methods is a new transversality theorem theorem 1 16

parallelized structures for mimo fbmc under strong channel frequency selectivity a novel architecture for mimo transmission and reception of filterbank multicarrier fbmc modulated signals under strong frequency selectivity is presented the proposed system seeks to approximate an ideal frequency selective precoder and linear receiver by taylor expansion exploiting the structure of the analysis and synthesis filterbanks the resulting architecture is implemented by linearly combining conventional mimo linear transceivers which are applied to sequential derivatives of the original filterbank the classical per subcarrier precoding linear receiver configuration is obtained as a special case of this architecture when only one stage is fixed at both transmitter and receiver an asymptotic expression for the resulting intersymbol intercarrier isi ici distortion is derived assuming that the number of subcarriers grows large this expression can in practice be used in order to determine the number of parallel stages that need to be implemented in the proposed architecture performance evaluation studies confirm the substantial advantage of the proposed scheme in practical frequency selective mimo scenarios

difference equations isoperimetric inequality and transience of certain random walks the difference laplacian on a square lattice in rn has been stud ied by many authors in this paper an analogous difference operator is studied for an arbitrary graph it is shown that many properties of the laplacian in the continuous setting e g the maximum principle the harnack inequality and cheeger s bound for the lowest eigenvalue hold for this difference oper ator the difference laplacian governs the random walk on a graph just as the laplace operator governs the brownian motion as an application of the theory of the difference laplacian it is shown that the random walk on a class of graphs is transient the random walks we consider are defined as follows let k be a connected graph i e a one dimensional simplicial complex for a vertex x e k let m x denote the number of edges emanating from x the probability that a particle moves from x to another vertex y e k is l m x if x and y are connected by an edge and it is zero otherwise as observed by courant friedrichs and lewy cfl for the case of a square lattice in the plane this random walk is intimately related to the difference analog of the laplacian

whitehead groups and the bass conjecture this paper will be concerned with proving that certain whitehead groups of torsion free elementary amenable groups are torsion groups and related results and then applying these results to the bass conjecture in particular we shall establish the strong bass conjecture for an arbitrary elementary amenable group

geometric transfer and the homotopy type of the automorphism groups of a manifold introduction for m a compact manifold with or without boundary in one of the categories diff pl or top we denote by a m the semisimplicial ss group of automorphisms of m i e the group of diffeomorphisms pl homeomorphisms or homeomorphisms resp in this paper we describe in the stability range and localized away from two the homotopy structure of a m we do this in terms of a m the ss group of block automorphisms whose homotopy structure is a sophisticated formulation of surgery theory abk and some new homotopy functors 5 theorem c the functors 5 and 5 l here considered have already been studied in the pl category by hatcher h from a different point of view the present geometric description is appropriate to the description of the homotopy structure of a m and enables us to produce a natural map b sc x 5 x from the associative monoid of simple homotopy equivalence of x to 5 x which will be important for our study besides the geometric topology results blr two ideas partially developed in bli are basic the first is the transfer map and stability for concordances described in the pl context by hatcher and in the differentiable context in bli the second is the splitting of a z 1 weak commutative topological group with involution as a product up to homotopy of two pieces the symmetric respectively antisymmetric parts applied to our situation those parts manifest very different behavior the results of this paper have been sketched by the first author in the survey paper b there is an overlap between some but not all results of a and results of hatcher h2 published in the same volume as b the results of this paper are stated in the next section statement of results and the proofs are given in subsequent sections we continue this section with a description of the notations used

recognition of linear actions on spheres let g be a finite group acting smoothly on a homotopy sphere ym we wish to establish necessary and sufficient conditions for the given g action on i to be topologically equivalent to a linear action that is we want to be able to decide whether or not there exists a g homeomorphism y i sm p where sm p c r i p denotes the unit sphere in an orthogonal representation space r p for g in order for a g action on i to be topologically equivalent to a linear action it is clearly necessary that i for each subgroup h of g the fixed point set h is homeomorphic to a sphere or empty ii for any subgroups h and h c h i s i s k of g the pair h u i1lh is homeomorphic to a standard pair s uk is where each sr i s i s k is a standard n subsphere of sn in this paper we consider the case where the fixed point set eg is nonempty and all other fixed point sets have dimension at least 5 in giving efficient sufficient conditions we do not need the full strength of condition ii we only need ii for any subgroups h and h c h i s i s p of g such that dim ih dim h 2 the pair ih uft1 h is homeomorphic to a standard pair s n up sin 2 where each s0 2 1 s i s p is a standard n 2 subsphere of n our main results are then that in the case when g is abelian conditions i and ii are riecessary and sufficient for a given g action on i to be topologically equivalent to a linear action and in the case of an action of an arbitrary finite group the same holds under the additional assumption that any simultaneous codimension i and 2 fixed point situation is simple our results generalize for actions of finite groups a well known theorem of connell montgomery and yang and are the first to also cover the case where codimension 2 fixed point situations occur let g be a finite group acting smoothly on a homotopy sphere 2m a homotopy sphere 2m is a smooth manifold which is homeomorphic to sm we wish to establish necessary and sufficient conditions for the given g action on l to be topologically equivalent to a linear action that is we want to be able to decide whether or not there exists a g homeomorphism y l sm p where sm p c rn l p denotes the unit sphere in an orthogonal representation space rn l p for g in order for a given g action on l to be topologically equivalent to a linear action it is clearly necessary that the following two conditions hold i for each subgroup h of g the fixed point set 2h is homeomorphic to a sphere or empty received by the editors january 7 1981 1980 mathematics subject classification primary 57s17 57s25 secondary 57q30

the rate of escape for anisotropic random walks in a tree let g be the group generated by l free involutions whose cayley graph t is the infinite homogeneous tree with l edges at every node a general central limit theorem and law of the iterated logarithm is proven for left invariant random walks z n on g or t which applies to the distance of z n from a fixed point as well as to the distribution of the last r letters in z n for nearest neighbor random walks we also derive a generating function identity that yields formulas for the asymptotic mean and variance of the distance from a fixed point a generalization for z n with a finitely supported step distribution is derived and discussed

algebraic k theory of virtually free groups we provide a general procedure for computing the algebraic k theory of finitely generated virtually free groups the procedure describes these groups in terms of the algebraic k theory of various finite subgroups and various farrell nil groups we illustrate this process by carrying out the computation for several interesting classes of examples the first two classes serve as a check on the method and show that our algorithm recovers results that already exist in the literature the last two classes of examples yield new computations

k theory and dynamics i un theoreme de h cobordisme avec commande feuillettee la variete associee le transfert asymptotique dynamique du flot geodesique completion de la demonstration du theoreme principal revue de la theorie de la commande structures de longues cellules minces

isomorphism conjectures in algebraic k theory duff in this paper we are concerned with the four functors y y3 if and which map from the category of topological spaces x to the category diff of q spectra the functor 3 or if maps the space x to the qspectrum of stable topological or smooth pseudoisotopies of x the spaces diff dif 3i x id9 x i 0 are hatcher s deloopings of 970 x yd x cf 29 the functor j maps a path connected space x to the algebraic ktheoretic s2 spectrum for the integral group ring z7r1x the spaces x x i 0 are the gersten wagoner deloopings of z o x cf 27 52 5 x is also defined on a nonpath connected space x to be x1 where xi i e i are the path components of x and ii xi indicates the direct limit of all finite products of the i xi i e i if x is path connected then the functor maps x to the l surgery classifying spaces for oriented surgery problems with fundamental group r i1x identified by their fourfold periodicity k 90 x k 4j x cf 35 39 44 47 in addition if x is not path connected then we set y77 x tiei5 fj xi where xi i e i are the path components of x results obtained by the authors over the past five years cf 15 25 and in particular 19 16 a 1 a 18 together with many earlier results and conjectures which are reviewed in 1 6 1 1 6 6 suggest that for any connected cwcomplex x and for 5 denoting any of the above functors the q spectrum x should be computable in a simple way from the values taken by 9 on covering spaces of x which have very simple fundamental groups in more detail we let 9 x denote the collection of all subgroups h c ir ix which are either finite or virtually infinite cyclic a group h is virtually infinite cyclic if there is a short exact sequence of groups 1 z h f 1 with f equal to a finite group and z equal to the infinite cyclic group for each such group we let xh x denote the covering space projection corresponding to h then the q spectrum 5 x should be computable in a simple way from the q spectra 5 xh h e 9 x the purpose of this paper is to formulate precisely a conjecture along these lines and to verify the conjecture for any x

the lifting problem for affine structures in nilpotent lie groups affine manifolds occur in several situations in pure and applied mathematics e g leaves of lagrangian foliations completely integrable hamiltonian systems linear representations of virtually polycyclic groups geometric quantization and so on this work is devoted to left invariant affinely flat structures in lie groups we are mainly concerned with the following situation let g and go be nilpotent lie groups of dimension n 1 and n respectively and let h g p go be a continuous homomorphism from g onto go given a left invariant affinely flat structure go vo the lifting problem is to discover whether g has a left invariant affinely flat structure g v such that h becomes an affine morphism in the present work we answer positively when go vo is normal therefore the existence problem for a left invariant complete affinely flat structure in nilpotent lie groups is solved by applying the following subsequent results let tf go be the set of left invariant affinely flat structures in the nilpotent lie group go 10 tf go 0 implies the existence of normal structure go vo e tf go 20 h g go being as above every normal structure go v0 has a normal lifted in atf g

martin and end compactifications for non locally finite graphs we consider a connected graph having countably infinite vertex set x which is permitted to have vertices of infinite degree for a transient irreducible transition matrix p corresponding to a nearest neighbor random walk on x we study the associated harmonic functions on x and in particular the martin compactification we also study the end compactification of the graph when the graph is a tree we show that these compactifications coincide they are a disjoint union of x the set of ends and the set of improper vertices new points associated with vertices of infinite degree other results proved include a solution of the dirichlet problem in the context of the end compactification of a general graph applications are given to e g the cayley graph of a free group on infinitely many generators

bounded homotopy equivalences of hilbert cube manifolds let m and f be hubert cube manifolds with f compact the purpose of this paper is to study homotopy equivalences m r x f which have bounded control in the redirection roughly these homotopy equivalences form a semi sim plicial complex 4 rm x f the controlled whitehead space using results about approximate fibrations rm x f is related to the semi simplicial complex of bounded concordances on r x f then the homotopy groups of rm x f are computed in terms of the lower algebraic at theoretic functors k i 1 introduction let f be a compact hilbert cube manifold we are interested in homotopy equivalences m rm x f which are controlled in the redirection where m is also a hilbert cube manifold to say is controlled in the redirection means that pf m rm is an approximate fibration where p rm x f rm is projection the collection of all such homotopy equivalences which are additionally given to be retractions onto the collared submanifold rm x f of m form the vertices of a semi simplicial complex ta rm x f see 2 for the precise definition the main result of this paper is the computation of the homotopy groups of wa rm x f see corollary 1 below in order to do this we relate wa rm x f to the semi simplicial complex h rm x f of bounded concordances on rm x f an simplex of eb rm x f is a homeomorphism

higher dimensional manifolds with s1 category 2 a closed topological n manifold mn is of s1 category 2 if it can be covered by two open subsets w1 w2 such that the inclusions wi mn factor homotopically through maps wi s1 we show that for n 3 if rm cat s 1 m n 2 then mn is homeomorphic to sn or sn 1 s1 or the non orientable sn 1 bundle over s1 we also obtain an unknotting theorem for locally flat knots of sn 2 in sn and a characterization of s1 sn 1

group actions and equivariant lipschitz analysis the idea that one could prove by analytic methods the topological invariance of characteristic classes was suggested in an influential lecture by singer the concrete realization of this in the case of rational pontrjagin classes was the result of works by sullivan who showed that topological manifolds have essentially unique lipschitz structures and teleman who showed that lipschitz manifolds are the type of object for which one can analyze the signature operator a refinement of the same method proves the ko l 2 orientability of topological bundles much of this can be done for manifolds with group actions the main implication is that for certain sorts of topological group actions including all smooth and pl actions one can construct an equivariant signature operator whose class in equivariant if homology is a topological invariant this class satisfies the g signature theorem the topological method has implications for various precise classification problems e g semifree topological actions on the sphere but here we shall present only the consequences of these lipschitzian ideas a topologically locally linear g manifolds for odd order g have kog 1 2 orientations madsen rothenberg for all finite g there are lipschitz structures but the signature class is a zero divisor for even order groups the same method produces upon application of the localization theorem atiyah singer classes for some actions with nonmanifold fixed set weinberger extending earlier joint work with cappell b for odd order groups topological and linear conjugacy of linear representations are equivalent hsiang pardon madsen rothenberg this is a consequence of a alternatively one can return to the original argument of atiyah bott milnor for semifree representations a stronger result is true the atiyah bott local numbers associated to representations agree for elements that have discrete fixed sets in topologically equivalent representations this distinguishes many pairs of representations of even order groups c r top g r lip g for all finite g where r cat is the grothendieck group of representations up to cat conjugacy weinberger after inverting 2 this implies that there is no analytic definition of reidemeister torsion that works well in the lipschitz setting the reason is that following

on the farrell jones conjecture for higher algebraic k theory here b is the classifying space of the group and we denote by k r the non connective algebraic k theory spectrum of the ring r the homotopy groups of this spectrum are denoted kn r and coincide with quillen s algebraick groups of r qui73 in positive dimensions and with the negative k groups of bass bas68 in negative dimensions the homotopy groups of the spectrum x k r are denotedhn x k r they yield a generalized homology theory and in particular standard computational tools such as the atiyah hirzebruch spectral sequence apply to the left hand side of the assembly map above as a corollary of the main result of this paper we prove conjecture 1 1 in the case where is the fundamental group of a closed riemannian manifold with strictly negative sectional curvature in fact our result is more general and applies to group rings r where r is a completely arbitrary coefficient ring note that if one replaces in conjecture 1 1 the coefficient ring z by an arbitrary coefficient ringr the corresponding conjecture would be false already in the simplest non trivial case if c is the infinite cyclic group the bass heller swan formula bhs64 gra76 p 236 for kn rc kn r t 1 yields that kn rc kn 1 r kn r nkn r nkn r where nkn r is defined as the cokernel of the split inclusion kn r kn r t and does not vanish in general but since s is a model for bc one obtains on the left hand side of the assembly map only hn bc k r kn r kn 1 r

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

single tap precoders and decoders for multiuser mimo fbmc oqam under strong channel frequency selectivity the design of linear precoders or decoders for multiuser multiple input multiple output filterbank multicarrier fbmc modulations in the case of a strong channel frequency selectivity is presented the users and the base station bs communicate using space division multiple access the low complexity proposed solution is based on a single tap per subcarrier precoding decoding matrix at the bs in the downlink uplink as opposed to classical approaches that assume flat channel frequency selectivity at the subcarrier level the bs does not make this assumption and takes into account the distortion caused by channel frequency selectivity the expression of the fbmc asymptotic mean squared error mse in the case of strong channel selectivity derived in earlier works is developed and extended the linear precoders and decoders are found by optimizing the mse formula under two design criteria namely zero forcing or minimum mse finally simulation results demonstrate the performance of the optimized design as long as the number of bs antennas is larger than the number of users it is shown that those extra degrees of freedom can be used to compensate for the channel frequency selectivity

approximately fibering a manifold over an aspherical one the paper is devoted to the problem when a map from some closed connected manifold to an aspherical closed manifold approximately fibers i e is homotopic to manifold approximate fibration we define obstructions in algebraic k theory their vanishing is necessary and under certain conditions sufficient basic ingredients are quinn s thin h cobordism theorem and end theorem and knowledge about the farrell jones conjectures in algebraic k and l theory and the maf rigidity conjecture by hughes taylor williams

the dirichlet problem at infinity for manifolds of negative curvature on considere l existence de fonctions harmoniques bornees sur des varietes simplement connexes n n de courbure negative