On the $\Sigma$-invariants of wreath products

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.

Second version: Corrected stylistic issues; revised and extended some arguments in Sections 6-8. Results are the same

References in corpus (2)

• Notes on the Sigma invariants
• Homological finiteness properties of wreath products

Cited by in corpus (1)

• On the Bieri-Neumann-Strebel-Renz ${\Sigma }^1$-invariant of even Artin groups