Sigma theory for Bredon modules

  • Dessislava H. Kochloukova

    IMECC - UNICAMP, Campinas, Brazil
  • Conchita Martínez-Pérez

    Universidad de Zaragoza, Spain

Abstract

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

Cite this article

Dessislava H. Kochloukova, Conchita Martínez-Pérez, Sigma theory for Bredon modules. Groups Geom. Dyn. 8 (2014), no. 2, pp. 415–440

DOI 10.4171/GGD/232