## 96 Citations

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

- Mathematics
- 2012

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

- Mathematics
- 2014

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

- MathematicsInt. J. Algebra Comput.
- 2002

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

- Mathematics
- 2007

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

- Mathematics
- 1992

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

- Mathematics
- 2009

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

- Mathematics
- 1994

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,…

## References

SHOWING 1-10 OF 40 REFERENCES

### THE NONTRIVIALITY OF THE RESTRICTION MAP IN THE COHOMOLOGY OF GROUPS

- Mathematics
- 1960

An unpublished result2 of B. Mazur states that if ir is any nontrivial finite group then there is an i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

- Mathematics
- 1957

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,…

### HOMOLOGY OF THE INFINITE SYMMETRIC GROUP

- Mathematics
- 1961

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

- MathematicsProceedings 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…

### A REMARK ON GROUPS WITH TRIVIAL MULTIPLICATOR.

- Mathematics
- 1975

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

- MathematicsJournal of the Australian Mathematical Society
- 1973

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

- Mathematics
- 1950

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

- MathematicsProceedings of the Edinburgh Mathematical Society
- 1962

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

- MathematicsPhilosophical 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

- MathematicsMathematical 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…