The topology of discrete groups

  title={The topology of discrete groups},
  author={Gilbert Baumslag and Eldon Dyer and Alex Heller},
  journal={Journal of Pure and Applied Algebra},

On the Theorem of Kan-Thurston and Algebraic Rank of CAT(0) groups

This thesis is divided into two parts. In chapter 2, we study two generalizations of the Kan-Thurston theorem. The Kan-Thuston theorem says that every complex X has the homology of some group G. As a

Free and properly discontinuous actions of discrete groups on homotopy circles

Let G × Σ(1) × Σ(1) be a free, properly discontinuous and cellular action of a group G on a finite-dimensional CW-complex Σ(1) that has the homotopy type of the circle. We determine all virtually

New Invariants for Groups

This paper defines Alexander-type ideals for modules as well as a number of secondary group invariants in the form of polynomials and 'ranks', which are connected with work of Swan, Hattori and Stallings, S. Brown and Lustig.

Finite group extensions and the Atiyah conjecture

The Atiyah conjecture for a discrete group G states that the L 2 -Betti numbers of a finite CW-complex with fundamental group G are integers if G is torsion-free, and in general that they are

Groups and spaces with all localizations trivial

The genus of a finitely generated nilpotent group G is defined as the set of isomorphism classes of finitely generated nilpotent groups K such that the p-localizations Kp, Gp are isomorphic for all

2 7 Fe b 20 07 About a conjecture of

We give a counterexample to a conjecture of D.H. Gottlieb and prove a strengthened version of it. The conjecture says that a map from a finite CW-complex X to an aspherical CW-complex Y with non-zero

Recent advances in unstable localization

The essentials of localization of 1-connected spaces —or, more generally, nilpotent spaces— at a set of primes P were solidly established between 1970 and 1975. Since then, the monograph by Hilton,




An unpublished result2 of B. Mazur states that if ir is any nontrivial finite group then there is an i> 0 such that Hi(Qr, Z) $0. It is, course, trivial that Hi(ir, A) #0 for some ir-module A. The

On the Lusternik-Schnirelmann Category of Abstract Groups

Let H be an abstract group. The cohomology groups H'(1l, A) may then be considered for any integer q > 0 and any abelian group A with II as a group of operators. The least integer n such that H'(II,


H*(S(co); Z.,) with coefficients in the integers mod p (p :prime). It is proved that the height of any non-zero element is co if p = 2, and is either co or < p if p is odd. If p = 2 this fact and the

Finiteness conditions for CW complexes. Il

  • C. Wall
  • Mathematics
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1966
A CW complex is a topological space which is built up in an inductive way by a process of attaching cells. Spaces homotopy equivalent to CW complexes play a fundamental role in topology. In the


1. Ler Hn (G) denote the nth homology group of G (with trivial integral coefficients), The (Schur) multiplicator of G is then, by definition, H2(G). The object of this note is to construct infinitely

Some small aspherical spaces

Let Sn denote the sphere of all points in Euclidean space Rn + 1 at a distance of 1 from the origin and Dn + 1 the ball of all points in Rn + 1 at a distance not exceeding 1 from the origin The space

Cohomology Theory of Groups with a Single Defining Relation

The Word Problem is that of determining when two elements of F (or two 'words') represent the same element of G, or, equivalently, when a given element W of F lies in R, and so can be written in the

Embedding Theorems for Groups

By a partial endomorphism of a group G we mean a homomorphic mapping μ of a subgroup A of G onto a subgroup B of G. If μ is denned on the whole of G then it is called a total endomorphism. We call a

An essay on free products of groups with amalgamations

  • B. Neumann
  • Mathematics
    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1954
Free products of groups with amalgamated subgroups, first introduced by Schreier (1927) and generalized by Hanna Neumann (1948), are here redefined, studied and applied to a number of problems in

Resolutions for extensions of groups

  • C. Wall
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1961
Let G be an extension of the normal subgroup K by its quotient group H. Suppose we are given free resolutions for H, K (see below for definition). We shall show how to construct from them, by a