On the $\Sigma$-invariants of wreath products

Luis Augusto de Mendonça

Vol. 298 (2019), No. 1, 113–139

DOI: 10.2140/pjm.2019.298.113

Abstract

We present a full description of the Bieri–Neumann–Strebel invariant of restricted permutational wreath products of groups. We also give partial results about the $2$-dimensional homotopical invariant of such groups. These results may be turned into a full picture of these invariants when the abelianization of the basis group is infinite. We apply these descriptions to the study of the Reidemeister number of automorphisms of wreath products in some specific cases.

Keywords

sigma theory, wreath product, twisted conjugacy

Mathematical Subject Classification 2010

Primary: 20E22, 20F65

Secondary: 20E45

Milestones

Received: 15 September 2017

Revised: 15 May 2018

Accepted: 25 May 2018

Published: 2 February 2019