#### 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