Vol. 298, No. 1, 2019

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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
Authors
Luis Augusto de Mendonça
Department of Mathematics
University of Campinas (UNICAMP)
Campinas
Brazil