On algebraic characterizations for finiteness of the dimension of EG

Certain algebraic invariants of the integral group ring ZG of a group G were introduced and investigated in relation to the problem of extending the Farrell-Tate cohomology, which is defined for the class of groups of finite virtual cohomological dimension. It turns out that the finiteness of these...

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Bibliographic Details
Published in:Iranian journal of numerical analysis and optimization 2008-01, Vol.1 (1)
Main Author: Olympia Talelli
Format: Article
Language:English
Subjects:
classifying space for proper action
complete resolution
farrell-tate cohomology
finitistic dimension of the integral group ring
virtual cohomological dimension
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Summary:Certain algebraic invariants of the integral group ring ZG of a group G were introduced and investigated in relation to the problem of extending the Farrell-Tate cohomology, which is defined for the class of groups of finite virtual cohomological dimension. It turns out that the finiteness of these invariants of a group G implies the existence of a generalized Farrell-Tate cohomology for G which is computed via complete resolutions. In this article we present these algebraic invariants and their basic properties and discuss their relationship to the generalized Farrell-Tate cohomology. In addition we present the status of conjecture which claims that the finiteness of these invariants of a group G is equivalent to the existence of a finite dimensional model for EG, the classifying space for proper actions.
ISSN:2423-6977
2423-6969
DOI:10.22067/ijnao.v1i1.616