Groups, Geometry, and Dynamics

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Volume 8, Issue 2, 2014, pp. 415–440
DOI: 10.4171/GGD/232

Published online: 2014-07-08

Sigma theory for Bredon modules

Dessislava H. Kochloukova[1] and Conchita Martínez-Pérez[2]

(1) IMECC - UNICAMP, Campinas, Brazil
(2) Universidad de Zaragoza, Spain

We develop new invariants $\underline{\Sigma}^m(G, \underline{A})$ similar to the Bieri–Strebel–Neumann–Renz invariants $\Sigma^m(G, A)$ but in the category of Bredon modules $\underline{A}$ (with respect to the class of the finite subgroups of $G$). We prove that for virtually soluble groups of type $\operatorname{FP}_{\infty}$ and finite extension of the Thompson group $F$ we have $ \underline{\Sigma}^{\infty}(G, \underline{\mathbb Z}) = \Sigma^{\infty}(G, \mathbb Z)$.

Keywords: Bredon cohomology, Sigma theory

Kochloukova Dessislava, Martínez-Pérez Conchita: Sigma theory for Bredon modules. Groups Geom. Dyn. 8 (2014), 415-440. doi: 10.4171/GGD/232