Jumps in cohomology and free group actions

Details Jumps in cohomology and free group actions Jumps in cohomology and free group actions

2005-04-06

arxiv.org/abs/math/0504122v3

Journal of Pure and Applied Algebra 210 (2007) 695-703

Mathematics

Algebraic Topology

14 pages

Scientific paper

A discrete group G has periodic cohomology over R if there is an element in a cohomology group, cup product with which induces an isomorphism in cohomology after a certain dimension. Adem and Smith showed 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 di- mension. 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.

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