the novikov conjecture for algebraic k theory of the group algebra over the ring of schatten class operators abstract in this paper we prove the algebraic k theory novikov conjecture for group algebras over the ring of schatten class operators the main technical tool in the proof is an explicit construction of the connes chern character

algebraic k theory of group rings and the cyclotomic trace map we prove that the farrell jones assembly map for connective alge braic k theory is rationally injective under mild homological niteness condi tions on the group and assuming that a weak version of the leopoldt schneider conjecture holds for cyclotomic elds this generalizes a result of bokstedt hsiang and madsen and leads to a concrete description of a large direct summand of kn z g z q in terms of group homology in many cases the number theoretic conjectures are true so we obtain rational injectivity results about assembly maps in particular for whitehead groups under niteness assumptions on the group only the proof uses the cyclotomic trace map to topological cyclic homology bokstedt hsiang madsen s functor c and new general injectivity results about the assembly maps for topological hochschild homology and c

low distortion embeddings of graphs with large girth the main purpose of the paper is to construct a sequence of graphs of constant degree with indefinitely growing girths admitting embeddings into l1 with uniformly bounded distortions this result solves the problem posed by n linial a magen and a naor 2002

the angular metric traveling salesman problem motivated by applications in robotics we formulate the problem of minimizing the total angle cost of a tsp tour for a set of points in euclidean space where the angle cost of a tour is the sum of the direction changes at the points we establish the np hardness of both this problem and its relaxation to the cycle cover problem we then consider the issue of designing approximation algorithms for these problems and show that both problems can be approximated to within a ratio of o log n in polynomial time we also consider the problem of simultaneously approximating both the angle and the length measure for a tsp tour in studying the resulting tradeoff we choose to focus on the sum of the two performance ratios and provide tight bounds on the sum finally we consider the extremal value of the angle measure and obtain essentially tight bounds for it in this paper we restrict our attention to the planar setting but all our results are easily extended to higher dimensions

coarsely embeddable metric spaces without property a abstract we study guoliang yu s property a and construct metric spaces which do not satisfy property a but embed coarsely into the hilbert space

ideal structure of uniform roe algebras of coarse spaces abstract let c u x e be the uniform roe algebra of a coarse space x e with uniformly locally finite coarse structure by a controlled truncation technique we show that the controlled propagation operators in an ideal i of c u x e are exactly the controlled truncations of elements in i it follows that the lattice of the ideals of the uniform roe algebra c u x e in which controlled propagation operators are dense the lattice of the invariant open subsets in the unit space of the groupoid g x introduced by skandalis tu and yu the lattice of the ideals of the coarse structure e and the lattice of the ideals of the coarse space x are mutually isomorphic these lattices also give rise to a type of classification for the ideals of c u x e

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

coarse baum connes conjecture and rigidity for roe algebras abstract in this paper we connect the rigidity problem and the coarse baum connes conjecture for roe algebras in particular we show that if x and y are two uniformly locally finite metric spaces such that their roe algebras are isomorphic then x and y are coarsely equivalent provided either x or y satisfies the coarse baum connes conjecture with coefficients it is well known that coarse embeddability into a hilbert space implies the coarse baum connes conjecture with coefficients on the other hand we provide a new example of a finitely generated group satisfying the coarse baum connes conjecture with coefficients but which does not coarsely embed into a hilbert space

the integral k theoretic novikov conjecture for groups with finite asymptotic dimension the integral assembly map in algebraic k theory is split injective for any geometrically finite discrete group with finite asymptotic dimension

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

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

un renforcement de la propriete t nous proposons un renforcement de la propriete t de kazhdan en remplacant les representations unitaires par les representations dans des espaces de hilbert qui ne sont pas necessairement unitaires mais a croissance exponentielle suffisamment petite on sait qu un groupe localement compact a la propriete t si et seulement si il existe un idempotent p dans c max g tel que pour toute representation unitaire continue h de g p est le projecteur orthogonal sur le sous espace ferme de h forme des vecteurs ginvariants pour la propriete t renforcee nous posons une definition dans ce style on appelle longueur sur un groupe localement compact g une fonction continue g r verifiant g 1 g et g1g2 g1 g2 pour g g1 g2 g dans la suite pour tout groupe localement compact g on supposera choisie une mesure de haar a gauche qui munit cc g d une structure d algebre par convolution

lower bounding procedure for the asymmetric quadratic traveling salesman problem abstract in this paper we consider the asymmetric quadratic traveling salesman problem aqtsp given a directed graph and a function that maps every pair of consecutive arcs to a cost the problem consists in finding a cycle that visits every vertex exactly once and such that the sum of the costs is minimal we propose an extended linear programming formulation that has a variable for each cycle in the graph since the number of cycles is exponential in the graph size we propose a column generation approach moreover we apply a particular reformulation linearization technique on a compact representation of the problem and compute lower bounds based on lagrangian relaxation we compare our new bounds with those obtained by some linearization models proposed in the literature computational results on some set of benchmarks used in the literature show that our lower bounding procedures are very promising

using a mixed integer quadratic programming solver for the unconstrained quadratic 0 1 problem in this paper we consider problem p of minimizing a quadratic function q x x tqx ctx of binary variables our main idea is to use the recent mixed integer quadratic programming miqp solvers but for this we have to first convexify the objective function q x a classical trick is to raise up the diagonal entries of q by a vector u until q diag u is positive semidefinite then using the fact that xi2 xi we can obtain an equivalent convex objective function which can then be handled by an miqp solver hence computing a suitable vector u constitutes a preprocessing phase in this exact solution method we devise two different preprocessing methods the first one is straightforward and consists in computing the smallest eigenvalue of q in the second method vector u is obtained once a classical sdp relaxation of p is solved we carry out computational tests using the generator of pardalos and rodgers 1990 and we compare our two solution methods to several other exact solution methods furthermore we report computational results for the max cut problem

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

on the dimension growth of groups we prove that the thompson group f has exponential dimension growth we also prove that every solvable finitely generated subgroup of f has polynomial dimension growth while some elementary amenable subgroups of f and some solvable groups of class 3 have dimension growth at least exp n

on banach spaces with kasparov and yu s property h abstract a new geometric property of banach spaces recently introduced by g kasparov and g yu called property h has important applications to the strong novikov conjecture and the coarse novikov conjecture yet is far from being well understood in this paper we investigate various uniformly continuous maps on unit spheres of banach spaces and prove that all separable banach lattices with nontrivial cotype have property h

optimal location of actuators for correcting distortions in large truss structures the paper suggests a continuum approximation to the statistical analysis first a continuum approximation to the calculation of statistical properties of the distorted and corrected shape of a statically determinate planar truss beam is compared to the exact calculation next the locations of the actuators are optimized to minimize the weighted rms of the distortion

large riemannian manifolds which are flexible for each k z we construct a uniformly contractible metric on euclidean space which is not mod k hypereuclidean we also construct a pair of uniformly contractible riemannian metrics on r n n 11 so that the resulting manifolds z and z are bounded homotopy equivalent by a homotopy equivalence which is not boundedly close to a homeomorphism we show that for these spaces the c algebra assembly map k lf z k c z from locally finite k homology to the k theory of the bounded propagation algebra is not a monomorphism this shows that an integral version of the coarse novikov conjecture fails for real operator algebras if we allow a single cone like singularity a similar construction yields a counterexample for complex c algebras

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

a quasi local characterisation of lp roe algebras abstract very recently spakula and tikuisis provide a new characterisation of uniform roe algebras via quasi locality when the underlying metric spaces have straight finite decomposition complexity in this paper we improve their method to deal with the l p version of uniform roe algebras for any p 1 due to the lack of reflexivity on l 1 spaces some extra work is required for the case of p 1

small cancellation theory over burnside groups abstract we develop a version of small cancellation theory in the variety of burnside groups more precisely we show that there exists a critical exponent n 0 such that for every odd integer n n 0 the well known classical c 1 6 small cancellation theory as well as its graphical generalization and its version for free products produce examples of infinite n periodic groups our result gives a powerful tool for producing uncountable collections of examples of n periodic groups with prescribed properties it can be applied without any prior knowledge in the subject of n periodic groups as applications we show the undecidability of markov properties in classes of n periodic groups we produce n periodic groups whose cayley graph contains an embedded expander graphs and we give an n periodic version of the rips construction we also obtain simpler proofs of some known results like the existence of uncountably many finitely generated n periodic groups and the sq universality in the class of n periodic groups of free burnside groups

coarse non amenability and covers with small eigenvalues given a closed riemannian manifold m and a virtual epimorphism pi 1 m twoheadrightarrow mathbb f 2 of the fundamental group onto a free group of rank 2 we construct a tower of finite sheeted regular covers left m n right n 0 infty of m such that 1 mn 0 as n this is the first example of such a tower which is not obtainable up to uniform quasi isometry or even up to uniform coarse equivalence by the previously known methods where 1 m is supposed to surject onto an amenable group

statistical analysis of static shape control in space structures the article addresses the problem of efficient analysis of the statistics of initial and corrected shape distortions in space structures two approaches for improving efficiency are considered one is an adjoint technique for calculating distortion shapes the second is a modal expansion of distortion shapes in terms of pseudo vibration modes the two techniques are applied to the problem of optimizing actuator locations on a 55 m radiometer antenna the adjoint analysis technique is used with a discrete variable optimization method the modal approximation technique is coupled with a standard conjugate gradient continuous optimization method the agreement between the two sets of results is good validating both the approximate analysis and optimality of the results

cones of matrices and set functions and 0 1 optimization it has been recognized recently that to represent a polyhedron as the projection of a higher dimensional but simpler polyhedron is a powerful tool in polyhedral combinatorics a general method is developed to construct higher dimensional polyhedra or in some cases convex sets whose projection approximates the convex hull of 0 1 valued solutions of a system of linear inequalities an important feature of these approximations is that one can optimize any linear objective function over them in polynomial time in the special case of the vertex packing polytope a sequence of systems of inequalities is obtained such that the first system already includes clique odd hole odd antihole wheel and orthogonality constraints in particular for perfect and many other graphs this first system gives the vertex packing polytope for various classes of graphs including t perfect graphs it follows that the stable set polytope is the projection of a polytope with a polynomial number of facets an extension o

on homological coherence of discrete groups abstract we explore a weakening of the coherence property of discrete groups studied by f waldhausen the new notion is defined in terms of the coarse geometry of groups and should be as useful for computing their k theory we prove that a group of finite asymptotic dimension is weakly coherent in particular there is a large collection of r modules of finite homological dimension when r is a finite dimensional regular ring this class contains word hyperbolic groups coxeter groups and as we show the cocompact discrete subgroups of connected lie groups

enhanced negative type for finite metric trees abstract a finite metric tree is a finite connected graph that has no cycles endowed with an edge weighted path metric finite metric trees are known to have strict 1 negative type in this paper we introduce a new family of inequalities 1 that encode the best possible quantification of the strictness of the non trivial 1 negative type inequalities for finite metric trees these inequalities are sufficiently strong to imply that any given finite metric tree t d must have strict p negative type for all p in an open interval 1 1 where 0 may be chosen so as to depend only upon the unordered distribution of edge weights that determine the path metric d on t in particular if the edges of the tree are not weighted then it follows that depends only upon the number of vertices in the tree we also give an example of an infinite metric tree that has strict 1 negative type but does not have p negative type for any p 1 this shows that the maximal p negative type of a metric space can be strict

quantitative geometry rather than describing a traditional field of mathematics quantitative geometry refers to a modern way of thinking about geometry and its applications that occur in a wide range of mathematical disciplines the overarching theme here is that certain geometric problems can only be formulated after the introduction of auxiliary quantitative parameters and asking for their asymptotic or approximate behavior this leads to meaningful questions that do not necessarily have counterparts in classical qualitative geometric investigations a viewpoint that allows one to uncover deep and useful structural information that appears only in the quantitative regime quantitative reasoning allows one to tame complicated objects and phenomena that are unwieldy if one insists on exact measurements it is often the case that a rich yet structured picture emerges only if one asks the correct questions by allowing for controlled errors

constructions preserving hilbert space uniform embeddability of discrete groups uniform embeddability in a hilbert space introduced by gromov is a geometric property of metric spaces as applied to countable discrete groups it has important consequences for the novikov conjecture exactness introduced and studied extensively by kirchberg and wassermann is a functional analytic property of locally compact groups recently it has become apparent that as properties of countable discrete groups uniform embeddability and exactness are closely related we further develop the parallel between these classes by proving that the class of uniformly embeddable groups shares a number of permanence properties with the class of exact groups in particular we prove that it is closed under direct and free products with and without amalgam inductive limits and certain extensions

on hypersphericity of manifolds with finite asymptotic dimension we prove the following embedding theorems in the coarse geometry theorem a every metric space x with bounded geometry whose asymptotic dimension does not exceed n admits a large scale uniform embedding into the product of n 1 locally finite trees corollary every metric space x with bounded geometry whose asymptotic dimension does not exceed n admits a large scale uniform embedding into a non positively curved manifold of dimension 2n 2 the corollary is used in the proof of the following theorem b for every uniformly contractible manifold x whose asymptotic dimension is finite the product x x r is integrally hyperspherical for some n theorem b together with a theorem of gromov lawson implies the result previously proven by g yu 1998 which states that an aspherical manifold whose fundamental group has a finite asymptotic dimension cannot carry a metric of positive scalar curvature we also prove that if a uniformly contractible manifold x of bounded geometry is large scale uniformly embeddable into a hilbert space then x is stably integrally hyperspherical

property a and affine buildings abstract yu s property a is a non equivariant generalisation of amenability introduced in his study of the coarse baum connes conjecture in this paper we show that all affine buildings of type a 2 b 2 and g 2 have property a together with results of guentner higson and weinberger this completes a programme to show that all affine building have property a in passing we use our technique to obtain a new proof for groups acting on a n buildings

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

the coarse geometric novikov conjecture for subspaces of non positively curved manifolds abstract in this paper we prove the coarse geometric novikov conjecture for metric spaces with bounded geometry which admit a coarse embedding into a simply connected complete riemannian manifold of non positive sectional curvature

optimal shape design of lattice structures for accuracy conclusion we found a free warping function of a beam of circular section acted upon by a torque in the direction of one of the axes of orthotropy it occurs two shearing modulus the result is just as it is an interesting one but may also be used for the experimental determination of shearing modulus making three tests of torsion in the three directions of orthotropy so calling x y z the three unknown modulus and a b c 0 2o o the three experimental results it would be necessary to solve the nonlinear system

box spaces group extensions and coarse embeddings into hilbert space abstract we investigate how coarse embeddability of box spaces into hilbert space behaves under group extensions in particular we prove a result which implies that a semidirect product of a finitely generated free group by a finitely generated residually finite amenable group has a box space which coarsely embeds into hilbert space this provides a new class of examples of metric spaces with bounded geometry which coarsely embed into hilbert space but do not have property a generalising the example of arzhantseva guentner and spakula

the boolean quadric polytope some characteristics facets and relatives we study unconstrained quadratic zero one programming problems havingn variables from a polyhedral point of view by considering the boolean quadric polytope qpn inn n 1 2 dimensions that results from the linearization of the quadratic form we show that qpn has a diameter of one descriptively identify three families of facets of qpn and show that qpn is symmetric in the sense that all facets of qpn can be obtained from those that contain the origin by way of a mapping the naive linear programming relaxation qpnlp of qpn is shown to possess the trubin property and its extreme points are shown to be 0 1 2 1 valued furthermore o n3 facet defining inequalities of qpn suffice to cut off all fractional vertices of qpnlp whereas the family of facets described by us has at least o 3n members the problem is also studied for sparse quadratic forms i e when several or many coefficients are zero and conditions are given for the previous results to carry over to this case polynomially solvable problem instances are discussed and it is shown that the known polynomiality result for the maximization of nonnegative quadratic forms can be obtained by simply rounding the solution to the linear programming relaxation in the case that the graph induced by the nonzero coefficients of the quadratic form is series parallel a complete linear description of the associated boolean quadric polytope is given the relationship of the boolean quadric polytope associated to sparse quadratic forms with the vertex packing polytope is discussed as well

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

finite decomposition complexity and the integral novikov conjecture for higher algebraic k theory decomposition complexity for metric spaces was recently introduced by guentner tessera and yu as a natural generalization of asymptotic dimension we prove a vanishing result for the continuously controlled algebraic k theory of bounded geometry metric spaces with finite decomposition complexity this leads to a proof of the integral k theoretic novikov conjecture regarding split injectivity of the k theoretic assembly map for groups with finite decomposition complexity and finite cw models for their classifying spaces by work of guentner tessera and yu this includes all geometrically finite linear groups

geometry of the mapping class groups i boundary amenability we construct a geometric model for the mapping class group mathcal m mathcal c mathcal g of a non exceptional oriented surface s of genus g with k punctures and use it to show that the action of mathcal m mathcal c mathcal g on the compact metrizable hausdorff space of complete geodesic laminations for s is topologically amenable as a consequence the novikov higher signature conjecture holds for every subgroup of mathcal m mathcal c mathcal g

relative property a and relative amenability for countable groups abstract we define a relative property a for a countable group with respect to a finite family of subgroups many characterizations for relative property a are given in particular a relative bounded cohomological characterization shows that if g has property a relative to a family of subgroups h and if each h h has property a then g has property a this result leads to new classes of groups that have property a in particular groups are of property a if they act cocompactly on locally finite property a spaces of bounded geometry with any stabilizer of property a specializing the definition of relative property a an analogue definition of relative amenability for discrete groups is introduced and similar results are obtained

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

an etale approach to the novikov conjecture we show that the rational novikov conjecture for a group of finite homological type follows from the mod 2 acyclicity of the higson compactification of an e we then show that for groups of finite asymptotic dimension the higson compactification is mod p acyclic for all p and deduce the integral novikov conjecture for these groups 2007 wiley periodicals inc

a metric approach to limit operators we extend the limit operator machinery of rabinovich roch and silbermann from z n to bounded geometry strongly discrete metric spaces we do not assume the presence of any group structure or action on our metric spaces using this machinery and recent ideas of lindner and seidel we show that if a metric space x has yu s property a then a band dominated operator on x is fredholm if and only if all of its limit operators are invertible we also show that this always fails for metric spaces without property a

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

a notion of geometric complexity and its application to topological rigidity we introduce a geometric invariant called finite decomposition complexity fdc to study topological rigidity of manifolds we prove for instance that if the fundamental group of a compact aspherical manifold m has fdc and if n is homotopy equivalent to m then m n is homeomorphic to n n for n large enough this statement is known as the stable borel conjecture on the other hand we show that the class of fdc groups includes all countable subgroups of gl n k for any field k

on exactness and isoperimetric profiles of discrete groups abstract we introduce a quasi isometry invariant related to property a and explore its connections to various other invariants of finitely generated groups this allows to establish a direct relation between asymptotic dimension on one hand and isoperimetry and random walks on the other we apply these results to reprove sharp estimates on isoperimetric profiles of some groups and to answer some questions in dimension theory

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

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

erratum on semidefinite programming relaxations of the traveling salesman problem we consider a new semidefinite programming sdp relaxation of the symmetric traveling salesman problem tsp that may be obtained via an sdp relaxation of the more general quadratic assignment problem qap we show that the new relaxation dominates the one in d cvetkovic m cangalovic and v kovacevic vujcic semidefinite programming methods for the symmetric traveling salesman problem in proceedings of the 7th international ipco conference on integer programming and combinatorial optimization springer verlag london uk 1999 pp 126 136 unlike the bound of cvetkovic et al the new sdp bound is not dominated by the held karp linear programming bound or vice versa

the symmetric quadratic traveling salesman problem in the quadratic traveling salesman problem a cost is associated with any three nodes traversed in succession this structure arises e g if the succession of two edges represents energetic conformations a change of direction or a possible change of transportation means in the symmetric case costs do not depend on the direction of traversal we study the polyhedral structure of a linearized integer programming formulation of the symmetric quadratic traveling salesman problem our constructive approach for establishing the dimension of the underlying polyhedron is rather involved but offers a generic path towards proving facetness of several classes of valid inequalities we establish relations to facets of the boolean quadric polytope exhibit new classes of polynomial time separable facet defining inequalities that exclude conflicting configurations of edges and provide a generic strengthening approach for lifting valid inequalities of the usual traveling salesman problem to stronger valid inequalities for the symmetric quadratic traveling salesman problem applying this strengthening to subtour elimination constraints gives rise to facet defining inequalities but finding a maximally violated inequality among these is np complete for the simplest comb inequality with three teeth the strengthening is no longer sufficient to obtain a facet preliminary computational results indicate that the new cutting planes may help to considerably improve the quality of the root relaxation in some important applications

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

reducing distortion and internal forces in truss structures by member exchanges manufacturing errors in the length of members or joint diameters of large truss reflector backup structures may result in unacceptable large distortion errors or member forces however it may be possible to accurately measure these length or diameter errors the present work suggests that a member and joint placement strategy may be used to reduce distortion errors and internal member forces a member and joint exchange algorithm is used to demonstrate the potential of this approach on several 102 member and 660 member truss reflector structures it is shown that it is possible to simultaneously reduce the rms of the surface error and the rms of member forces by two orders of magnitude by member and joint exchanges

on ozawa kernels we write explicitly ozawa kernels for group extensions for discrete metric spaces of finite asymptotic dimension of large enough hilbert space compression and for suitable actions of countable groups on metric spaces we also obtain an alternative proof of stability results concerning yu s property a

compression functions of uniform embeddings of groups into hilbert and banach spaces we construct finitely generated groups with arbitrary prescribed hilbert space compression alpha from the interval 0 1 for a large class of banach spaces e including all uniformly convex banach spaces the e compression of these groups coincides with their hilbert space compression moreover the groups that we construct have asymptotic dimension at most 3 hence they are exact in particular the first examples of groups that are uniformly embeddable into a hilbert space respectively exact of finite asymptotic dimension with hilbert space compression 0 are given these groups are also the first examples of groups with uniformly convex banach space compression 0

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

a generalization of expander graphs and local reflexivity of uniform roe algebras abstract we introduce a generalization of expander graphs which is called a weak expander sequence it is proved that a uniform roe algebra of a weak expander sequence is not locally reflexive it follows that uniform roe algebras of expander graphs are not exact we introduce the notion of a generalized box space to discuss box spaces and expander sequences in a unified framework key tools for the proof are amenable traces and measured groupoids associated with generalized box spaces

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