scholarly journals Normal subgroups in duality groups and in groups of cohomological dimension 2

1976 ◽  
Vol 7 (1) ◽  
pp. 35-51 ◽  
Author(s):  
Robert Bieri
Keyword(s):  
Cohomological Dimension ◽  
Normal Subgroups ◽  
Duality Groups ◽  
Dimension 2

BOUNDARY OF CAT(-1) COXETER GROUPS

1999 ◽  
Vol 09 (02) ◽  
pp. 169-178 ◽  
Author(s):  
N. BENAKLI
Keyword(s):  
Coxeter Groups ◽  
Cohomological Dimension ◽  
Existence Problem ◽  
Joint Work ◽  
Coxeter Graph ◽  
Combinatorial Properties ◽  
Jsj Decomposition ◽  
Complete Bipartite Graphs ◽  
Dimension 2 ◽  
Virtual Cohomological Dimension

In this paper, we study the topological properties of the hyperbolic boundaries of CAT(-1) Coxeter groups of virtual cohomological dimension 2. We will show how these properties are related to combinatorial properties of the associated Coxeter graph. More precisely, we investigate the connectedness, the local connectedness and the existence problem of local cut points. In the appendix, in a joint work with Z. Sela, we will construct the JSJ decomposition of the Coxeter groups for which the corresponding Coxeter graphs are complete bipartite graphs.

A group with zero homology

1968 ◽  
Vol 64 (3) ◽  
pp. 599-602 ◽  
Author(s):  
D. B. A Epstein
Keyword(s):  
Fundamental Group ◽  
Cohomological Dimension ◽  
Dimensional Manifold ◽  
Finitely Generated ◽  
3 Dimensional ◽  
Identity Group ◽  
Dimension 2

In this paper we describe a group G such that for any simple coefficients A and for any i > 0, Hi(G; A) and Hi(G; A) are zero. Other groups with this property have been found by Baumslag and Gruenberg (1). The group G in this paper has cohomological dimension 2 (that is Hi(G; A) = 0 for any i > 2 and any G-module A). G is the fundamental group of an open aspherical 3-dimensional manifold L, and is not finitely generated. The only non-trivial part of this paper is to prove that the fundamental group of the 3-manifold L, which we shall construct, is not the identity group.

scholarly journals NORMAL SUBGROUPS OF PROFINITE GROUPS OF FINITE COHOMOLOGICAL DIMENSION

2004 ◽  
Vol 69 (02) ◽  
pp. 317-332 ◽  
Author(s):  
A. ENGLER ◽  
D. HARAN ◽  
D. KOCHLOUKOVA ◽  
P. A. ZALESSKII
Keyword(s):  
Cohomological Dimension ◽  
Normal Subgroups ◽  
Profinite Groups

scholarly journals Subgroups of relatively hyperbolic groups of Bredon cohomological dimension 2

2017 ◽  
Vol 20 (6) ◽  
Author(s):  
Eduardo Martínez-Pedroza
Keyword(s):  
Cohomological Dimension ◽  
Hyperbolic Groups ◽  
Relatively Hyperbolic Groups ◽  
Remarkable Result ◽  
Dimension 2 ◽  
Relatively Hyperbolic ◽  
Finitely Presented

AbstractA remarkable result of Gersten states that the class of hyperbolic groups of cohomological dimension 2 is closed under taking finitely presented (or more generally

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