On algebraic characterizations for finiteness of the dimension of EG

Document Type : Research Article

Author

• Olympia Talelli

Department of Mathematics, University of Athens Panepistemiopolis, 15784 Athens - Greece

10.22067/ijnao.v1i1.616

Abstract

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.

Keywords

• Farrell-Tate cohomology
• virtual cohomological dimension
• complete resolution
• finitistic dimension of the integral group ring
• classifying space for proper action

20.1001.1.24236977.2008.1.1.1.6

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