Jumps in cohomology and free group actions
Jumps in cohomology and free group actions
A discrete group G has periodic cohomology over R if there is an element in a cohomology group cup product with which it induces an isomorphism in cohomology after a certain dimension. Adem and Smith showed that if R=Z, then this condition is equivalent to the existence of a finite dimensional free-G-CW-complex homotopy equivalent to a sphere. It has been conjectured by Olympia Talelli, that if G is also torsion-free then it must have finite cohomological dimension. In this paper we use the implied condition of jump cohomology over R to prove the conjecture for HF-groups and solvable groups. We also find necessary conditions for free and proper group actions on finite dimensional complexes homotopy equivalent to closed, orientable manifolds.
695-703
Petrosyan, Nansen
f169cfd6-aeee-4ad2-b147-0bf77dd1f9b6
September 2007
Petrosyan, Nansen
f169cfd6-aeee-4ad2-b147-0bf77dd1f9b6
Petrosyan, Nansen
(2007)
Jumps in cohomology and free group actions.
Journal of Pure and Applied Algebra, 210 (3), .
(doi:10.1016/j.jpaa.2006.11.011).
Abstract
A discrete group G has periodic cohomology over R if there is an element in a cohomology group cup product with which it induces an isomorphism in cohomology after a certain dimension. Adem and Smith showed that if R=Z, then this condition is equivalent to the existence of a finite dimensional free-G-CW-complex homotopy equivalent to a sphere. It has been conjectured by Olympia Talelli, that if G is also torsion-free then it must have finite cohomological dimension. In this paper we use the implied condition of jump cohomology over R to prove the conjecture for HF-groups and solvable groups. We also find necessary conditions for free and proper group actions on finite dimensional complexes homotopy equivalent to closed, orientable manifolds.
This record has no associated files available for download.
More information
Published date: September 2007
Organisations:
Pure Mathematics
Identifiers
Local EPrints ID: 356897
URI: http://eprints.soton.ac.uk/id/eprint/356897
PURE UUID: 7861a2b9-781d-41ba-9769-a07f4b53e8bb
Catalogue record
Date deposited: 21 Oct 2013 13:13
Last modified: 15 Mar 2024 03:49
Export record
Altmetrics
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
