homology and closure properties of autostackable groups abstract autostackability for finitely presented groups is a topological property of the cayley graph combined with formal language theoretic restrictions that implies solvability of the word problem the class of autostackable groups is known to include all asynchronously automatic groups with respect to a prefix closed normal form set and all groups admitting finite complete rewriting systems although groups in the latter two classes all satisfy the homological finiteness condition f p we show that the class of autostackable groups includes a group that is not of type f p 3 we also show that the class of autostackable groups is closed under graph products and extensions

on the knuth bendix completion for concurrent processes abstract we consider critical pairs for replacement systems over free partially commutative monoids this is done in order to apply the knuth bendix completion procedure to concurrent processes we will see that there are one rule systems which have no finite set of critical pairs therefore we develop a sufficient and computable condition such that finite trace replacement systems have a finite set of critical pairs this condition is always satisfied in the purely free case of semi thue systems or purely commutative case of vector replacement systems in fact it generalizes and unifies both cases we will give examples of how one can use this generalization

automorphisms of graph groups abstract given a graph v e the graph group on is the group generated by the vertex set v with the defining relations being that two adjacent vertices commute in the following the centralizer problem for graph groups is solved and it is shown that for some graph groups aut f is finitely generated by generators which are natural analogues to the nielsen automorphisms for a free group

the geometry of purely loxodromic subgroups of right angled artin groups we prove that finitely generated purely loxodromic subgroups of a right angled artin group a fulfill equivalent conditions that parallel characterizations of convex cocompactness in mapping class groups mod s in particular such subgroups are quasiconvex in a in addition we identify a milder condition for a finitely generated subgroup of a that guarantees it is free undistorted and retains finite generation when intersected with a for subgraphs of these results have applications to both the study of convex cocompactness in mod s and the way in which certain groups can embed in right angled artin groups

random dynamical systems generated by stochastic navier stokes equations on a rotating sphere abstract in this paper we first prove the existence and uniqueness of the solution to the stochastic navier stokes equations on the rotating 2 dimensional unit sphere then we show the existence of an asymptotically compact random dynamical system associated with the equations

on the consistency of bayes estimates on etudie les proprietes de frequence des regles de bayes avec une attention particuliere a la consistence

bounded rank subgroups of coxeter groups artin groups and one relator groups with torsion we obtain a number of results regarding the freeness of subgroups of coxeter groups artin groups and one relator groups with torsion in the case of coxeter groups we also obtain results on quasiconvexity and subgroup separability

generation of a section of conjugation classes and lyndon word tree of limited length resume etant donne un alphabet ordonne un mot de lyndon est un mot primitif qui est le plus petit dans sa classe de conjugaison nous donnons ici un algorithme qui construit dans l ordre la liste des mots de lyndon de longueur donnee cet algorithme est optimal en ce sens que le calcul du mot de lyndon suivant de la liste se fait en temps lineaire a partir du mot precedent et sans utilisation d une memoire auxiliaire cet algorithme trouve son application dans la construction d une section des classes de conjugaison d une longueur donnee c est une response a une question posee a l auter par m p schutzenberger

free partially commutative structures abstract in this paper we study algebraic structures defined by a presentation of the form a ab ba for a b i we show that these relators are the only one that can be interpreted as both monoid and lie relators we also study the free partially commutative monoids lie algebras and groups in all of these cases we show how to obtain decomposition results for these structures into the corresponding free structures

separable subsets of gferf negatively curved groups a word hyperbolic group g is called gferf if every quasiconvex subgroup coincides with the intersection of finite index subgroups containing it we show that in any such group the product of finitely many quasiconvex subgroups is closed in the profinite topology on g

on the support of graph lie algebras we deal with the support of graph lie algebras and we characterize the set of independence alphabets for which the noncommutative result can naturally be extended we also provide an algorithm which decides if an independence alphabet fulfills the preceding condition

consistent and robust bayes procedures for location based on partial information we consider bayes procedures for a location parameter that are robust with respect to the shape of the distribution f of the data the case where f is fixed and the case where f has a dirichlet distribution are both treated the procedures are based on the posterior distributions of the location parameter given the partial information contained in a robust estimate of location we show consistency and asymptotic normality of the procedures and give instances where the bayes procedure based on the full sample diverges while the bayes procedures based on partial information converges and is asymptotically normal

gevrey regularity for navier stokes equations under lions boundary conditions abstract the navier stokes system is considered in a compact riemannian manifold gevrey class regularity is proven under lions boundary conditions in 2d for the rectangle cylinder and hemisphere and in 3d for the rectangle the cases of the 2d sphere and 2d and 3d torus are also revisited

le complexe de chaines d un g complexe simplicial acyclique resume let g be a finite group the main result of this note shows that the reduced chain complex of an acyclic finite dimensional simplicial g complex is a split acyclic complex of z g modules the proof requires the extension of well known results on finitely generated p permutation modules to arbitrary p permutation modules the key is a theorem stating that a bounded complex of p permutation modules is split acyclic if and only if all its brauer quotients are acyclic

freudenthal triple systems by root system methods abstract for certain lie algebras g we can use a grading g g 2 g 1 g 0 g 1 g 2 and define a quartic form and a skew symmetric bilinear form on g 1 thereby constructing a freudenthal triple system the structure of the freudenthal triple system is examined using root system methods available in the lie algebra context in the cases g e 8 where g 1 is the minuscule representation of e 7 and g d 4 we determine the groups stabilizing the quartic form and both the quartic and bilinear forms

finiteness properties for subgroups of gl n mathbb z abstract we construct finitely presented subgroups of gl n mathbb z that have infinitely many conjugacy classes of finite subgroups this answers a question of grunewald and platonov we suggest a variation on their question

bayesian nonparametric estimation of the median part i computation of the estimates let x i i 1 ldots n be i i d sim f theta where f theta x f x theta for some f that has median equal to 0 f is assumed unknown or only partially known and the problem is to estimate theta priors are put on the pair f theta the priors on f concentrate all their mass on c d f s with median equal to 0 these priors include dirichlet type priors the marginal posterior distribution of theta given x 1 ldots x n is computed the mean of the posterior is taken as the estimate of theta

integrity of formal power series on a partially commutative alphabet resume nous demontrons que l anneau de series formelles sur un alphabet partiellement commutatif est integre

morse theory and finiteness properties of groups we examine the finiteness properties of certain subgroups of right angled artin groups in particular we find an example of a group that is of type fp z but is not finitely presented

cohomological finiteness conditions for mackey and cohomological mackey functors abstract we study cohomological finiteness conditions for groups associated to mackey and cohomological mackey functors proving that the cohomological dimension associated to cohomological mackey functors is always equal to the f cohomological dimension and characterising the conditions mackey fp n and cohomological mackey fp n

chern characters for proper equivariant homology theories and applications to k and l theory we construct for an equivariant homology theory for proper equiv ariant cw complexes an equivariant chern character provided that certain conditions are satisfied this applies for instance to the sources of the assembly maps in the farrell jones conjecture with respect to the family f of finite subgroups and in the baum connes conjecture thus we get an explicit calculation in terms of group homology of qn z knorgu and qn z lnorgu for a commutative ring r with qh r provided the farrell jones conjecture with respect to f is true and of qnz k top n c r og fu for fa r c provided the baum connes conjecture is true

parabolic and quasiparabolic subgroups of free partially commutative groups let be a finite graph and g be the corresponding free partially commutative group in this paper we study subgroups generated by vertices of the graph which we call canonical parabolic subgroups a natural extension of the definition leads to canonical quasiparabolic subgroups it is shown that the centralisers of subsets of g are the conjugates of canonical quasiparabolic centralisers satisfying certain graph theoretic conditions

separating quasiconvex subgroups of right angled artin groups a graph group or right angled artin group is a group given by a presentation where the only relators are commutators of the generators a graph group presentation corresponds in a natural way to a simplicial graph with each generator corresponding to a vertex and each commutator relator corresponding to an edge suppose that g is a graph group whose corresponding graph is a tree and h is a subgroup of g we show that if h is quasiconvex with respect to either the word metric on g or the cat 0 metric on the universal cover of the standard complex for g then h is separable that is h is the intersection of finite index subgroups of g we also discuss some consequences relating to certain 3 manifold groups

centralizers in graph products of groups abstract a graph product of groups is a construction which generalizes both free products and direct products of groups in this paper we study commuting elements in graph products of groups and find explicit formulas for the centralizer the subgroup consisting of elements which commute with a given element of elements of a graph product of groups in terms of the centralizers of elements in each vertex group and the structure of the graph

orthogonal projection onto the free lie algebra abstract as an answer to a question of garsia we give a universal formula in a normal form for the orthogonal projection of free associative algebra onto free lie algebra

artin groups of large type are shortlex automatic with regular geodesics we prove that any artin group of large type is shortlex automatic with respect to its standard generating set and that the set of all geodesic words over the same generating set satisfies the falsification by fellow traveller property fftp and hence is regular

on the profinite topology of right angled artin groups abstract in the present work we give necessary and sufficient conditions on the graph of a right angled artin group that determine whether the group is subgroup separable or not moreover we investigate the profinite topology of f 2 f 2 and we show that the profinite topology of the above group is strongly connected with the profinite topology of f 2

when is group cohomology finitary if g is a group then we say that the functor hn g is finitary if it commutes with all filtered colimit systems of coefficient modules we investigate groups with cohomology almost everywhere finitary that is groups with nth cohomology functors finitary for all sufficiently large n we establish sufficient conditions for a group g possessing a finite dimensional model for eg to have cohomology almost everywhere finitary we also prove a stronger result for the subclass of groups of finite virtual cohomological dimension and use this to answer a question of leary and nucinkis finally we show that if g is a locally polycyclic by finite group then g has cohomology almost everywhere finitary if and only if g has finite virtual cohomological dimension and the normalizer of every non trivial finite subgroup of g is finitely generated

euler classes and bredon cohomology for groups with restricted families of finite subgroups we explore some of the special features with respect to bredon cohomology for groups whose finite subgroups are all either nilpotent or p groups or cyclic p groups we get some results on dimensions and also a formula for the equivariant euler class for certain groups we consider the generalization for bredon cohomology of the properties of being duality or poincare duality and study their behavior under p power index extensions with coefficients in a field of characteristic p

linear preservers and representations with a 1 dimensional ring of invariants we determine the group of linear transformations on a vector space v that preserve a polynomial function f on v for several interesting pairs v f using the theory of semisimple algebraic groups in an 1897 paper fro97 frobenius proved that every linear transformation of the n by n real matrices that preserves the determinant is of the form x 7 axb or x 7 ax t b for some a b gln r such that det ab 1 this is the basic example of a linear preserver problem lpp one is given a finite dimensional vector space v over a field k and a polynomial function f v k and one wants to determine the linear transformations of v that preserve f since frobenius many such prob lems have been solved see for example the surveys lp01 pll 92 lt92 and mar62 we develop here a general method that solves several new problems see examples 3 14 and 3 15 and corollaries 7 10 8 3 8 7 8 5 8 8 and 8 11 our method is to introduce an auxiliary group g gl v that is semisimple and such that v is an irreducible representation or weyl module of g in section 2 we determine the normalizer ngl v g of g in gl v we prove in theorem 3 2 that this subgroup equals the stabilizer of a closed g orbit o in the projective space p v i e stabgl v o ngl v g using this result in sections 7 and 8 we solve two families of lpps by reducing the problems in each family to determining this stabilizer these two families consist of representations v with a 1 dimensional ring of g invariant functions generated by f and are examples of prehomogenous vector spaces of parabolic type the two families correspond to the cases where the unipotent radical u of the parabolic subgroup is abelian i e u u 0 or u u is 1 dimensional respectively and we use the general results on representations in these families from rrs92 roh93 and hel12 besides obtaining new results we also recover many known solutions to linear preserver problems the generality of our method is in contrast to many of the proofs in the literature which typically are highly dependent on the particular choice of v and f the arguments in pd95 and gur97 are notable exceptions further we require only very weak assumptions about the field k at most we require that the characteristic is 6 2 3 and determine the preserver precisely and not just its identity component or lie algebra

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

un critere de rationalite provenant de la geometrie non commutative we prove a conjecture of a connes which gives a rationality criterion for elements of the closure of a free group in the space of bounded operators in l 2 we show that this criterion applies also to the ring of malcev neumann series on

algorithms and geometry for graph products of groups recent work of gromov epstein cannon thurston and many others has generated strong interest in the geometric and algorithmic structure of finitely generated infinite groups see 16 17 and 14 many of these structures are preserved by taking graph products the graph product of groups not to be confused with the fundamental group of a graph of groups is a product mixing direct and free products whether the product between two groups in the graph product is free or direct is determined by a simplicial graph given a simplicial graph we say that two vertices are adjacent if they are joined by a single edge

cohomological finiteness conditions for elementary amenable groups it is proved that every elementary amenable group of type fp admits a cocompact classifying space for proper actions

a nonlinear galerkin scheme involving vector and tensor spherical harmonics for solving the incompressible navier stokes equation on the sphere this work is concerned with a nonlinear galerkin method for solving the incompressible navier stokes equation on the sphere it extends the work of a debussche t dubois and r temam theoret comput fluid dyn 7 1995 pp 279 315 m marion and r temam siam j numer anal 26 1989 pp 1139 1157 j shen and r temam proceedings of the international conference on nonlinear evolution partial differential equations ams providence ri 1997 pp 363 376 from one dimensional or toroidal domains to the spherical geometry in the first part the method based on type 3 vector spherical harmonics is introduced and convergence is indicated further it is shown that the occurring coupling terms involving three vector spherical harmonics can be expressed algebraically in terms of wigner 3j coefficients to improve the numerical efficiency and economy we introduce an fft based pseudospectral algorithm for computing the fourier coefficients of the nonlinear advection term the resulting method scales with o n 3 if n denotes the maximal spherical harmonic degree the latter is demonstrated in an extensive numerical example

bayesian estimation in the symmetric location problem let x i i for i 1 n where the i s are i i d f and f is symmetric about 0 f is assumed unknown or only partially known and the problem is to estimate priors are put on the pair f the priors on f are obtained from doksum s neutral to the right priors and include symmetrized dirichlet priors the marginal posterior distribution of given x1 xnis computed and its general properties studied it is found that for certain classes of distributions of the i s the posterior distribution of is for all large n a point mass at the true value of if the distribution of the i s is not exactly symmetric the bayes estimates can behave very poorly

embedddings between partially commutative groups two counterexamples abstract in this note we give two examples of partially commutative subgroups of partially commutative groups our examples are counterexamples to the extension graph conjecture and to the weakly chordal conjecture of kim and koberda 2013 12 on the other hand we extend the class of partially commutative groups for which it is known that the extension graph conjecture holds to include those with commutation graph containing no induced c 4 or p 3 in the process some new embeddings of surface groups into partially commutative groups emerge

symmetrical subgroups of artin groups we show that the subgroup fixed by a group of symmetries of an artin system a s is itself an artin group under the hypothesis that the deligne complex associated to a admits a suitable cat 0 metric such a metric is known to exist for all artin groups of type fc which include all the finite type artin groups as well as many infinite types we also recover the previously known analogous result for an arbitrary coxeter system w s

subgroups of graph groups given a graph x we define a group gx as follows gx is generated by the vertices of x with a defining relation xy jt for each pair y 2 of ver tices joined by an edge of x a group is called a graph group if it is isomorphic to gx for some graph x we will not distinguish by notation in what follows between a vertex of x and the corresponding element of gx we remark that the extreme cases of graphs namely the complete and the completely disconnected graphs correspond respectively to free abelian and free groups it is well known that any subgroup of a group of either of these types is again of the same type and it is thus natural to ask to what extent and in what form this is true of the graph groups that lie in between these extreme cases in this article we will prove the following

path lifting properties and embedding between raags abstract for a finite simplicial graph let g denote the right angled artin group on the complement graph of in this article we introduce the notions of induced path lifting property and semi induced path lifting property for immersions between graphs and obtain graph theoretical criteria for the embeddability between right angled artin groups we recover the result of s h kim and t koberda that an arbitrary g admits a quasi isometric group embedding into g t for some finite tree t the upper bound on the number of vertices of t is improved from 2 2 m 1 2 to m 2 m 1 where m is the number of vertices of we also show that the upper bound on the number of vertices of t is at least 2 m 4 lastly we show that g c m embeds in g p n for n 2 m 2 where c m and p n denote the cycle and path graphs on m and n vertices respectively

bayesian nonparametric estimation of the median part ii asymptotic properties of the estimates for data theta varepsilon i i 1 ldots n where varepsilon i are i i d sim f with the median of f equal to 0 but f otherwise unknown it is desired to estimate theta in doss 1985 priors are put on the pair f theta the marginal posterior distribution of theta is computed and the mean of the posterior is taken as the estimate of theta in the present paper a frequentist point of view is adopted the consistency properties of the bayes estimates computed in doss 1985 are investigated when the prior on f is of the dirichlet type any f whose median is 0 is in the support of these priors it is shown that if the varepsilon i are i i d from a discrete distribution then the bayes estimates are consistent however if the distribution of the varepsilon is is continuous the bayes estimates can be inconsistent

the free partially commutative lie algebra bases and ranks abstract in this paper we study the free partially commutative lie k algebra l a defined by a commutation relation on an alphabet a its behavior is very similar to that of the free lie algebra indeed we obtain in particular a partially commutative version of lazard s elimination process which allows us to prove that the k module l a is free and to construct explicitly k bases for it we show also how the classical witt s calculus can be extended to l a

on the geometry of normal forms in discrete groups we study normal forms in finitely generated groups from the geometric viewpoint of combings we introduce notions of combability considerably weaker than those commonly in use we prove that groups which satisfy these conditions are finitely presented and satisfy isoperimetric and isodiametric inequalities of a controlled nature

metric systolicity and two dimensional artin groups we introduce the notion of metrically systolic simplicial complexes we study geometric and large scale properties of such complexes and of groups acting on them geometrically we show that all two dimensional artin groups act geometrically on metrically systolic complexes as direct corollaries we obtain new results on two dimensional artin groups and all their finitely presented subgroups we prove that the conjugacy problem is solvable and that the dehn function is quadratic we also show several large scale features of finitely presented subgroups of two dimensional artin groups lying background for further studies concerning their quasi isometric rigidity

on dimensions of groups with cocompact classifying spaces for proper actions we construct groups g that are virtually torsion free and have virtual cohomological dimension strictly less than the minimal dimension for any model for the classifying space for proper actions of g they are the first examples that have these properties and also admit cocompact models for this classifying space we exhibit groups g whose virtual cohomological dimension and bredon cohomological dimension are two that do not admit any 2 dimensional contractible proper g cw complex

graph groups coherence and three manifolds 1 introou t n we study groups given by presentations each of whose defining relations is of the form ql yx for some generators y and y to such a presentation we associate a graph x whose vertices are the generators two vertices y and 1 being adjacent in x if and only if xy yx is a defining relation given a graph x we denote by gx the group defined by the presentation associated to x in this way we call gx a graph group these groups have been studied by kim and roush s and by dicks 3 in this paper we prove the following

rational computations of the topological k theory of classifying spaces of discrete groups we compute rationally the topological complex k theory of the classifying space bg of a discrete group provided that g has a cocompact g cw model for its classifying space for proper g actions for instance word hyperbolic groups and cocompact discrete subgroups of connected lie groups satisfy this assumption the answer is given in terms of the group cohomology of g and of the centralizers of finite cyclic subgroups of prime power order we also analyze the multiplicative structure

some groups of type vf a group is of type vf if it contains a finite index subgroup which has a finite classifying space we construct groups of type vf in which the centralizers of some elements of finite order are not of type vf and groups of type vf containing infinitely many conjugacy classes of finite subgroups from these examples it follows that a group g of type vf need not admit a finite type or finite classifying space for proper actions sometimes also called the universal proper g space we construct groups g for which the minimal dimension of a universal proper g space is strictly greater than the virtual cohomological dimension of g each of our groups embeds in some general linear group over the rational integers applications to algebraic k theory of group algebras and topological k theory of group c algebras are also considered the groups are constructed as finite extensions of bestvina brady groups

generalising some results about right angled artin groups to graph products of groups we prove three results about the graph product g g gv v v of groups gv over a graph the first result generalises a result of servatius droms and servatius proved by them for right angled artin groups we prove a necessary and sufficient condition on a finite graph for the kernel of the map from g to the associated direct product to be free one part of this result already follows from a result in s kim s phd thesis the second result generalises a result of hermiller and sunic again from right angled artin groups we prove that for a graph with finite chromatic number g has a series in which every factor is a free product of vertex groups the third result provides an alternative proof of a theorem due to meier which provides necessary and sufficient conditions on a finite graph for g to be hyperbolic

nonlinear galerkin methods this article presents a new method of integrating evolution differential equations the non linear galerkin method that is well adapted to the long term integration of such equations while the usual galerkin method can be interpreted as a projection of the considered equation on a linear space the methods considered here are related to the projection of the equation on a nonlinear manifold from the practical point of view some terms have been identified as small and sometimes but not always disregarded