Irreducible lattices fibring over the circle

Abstract

We investigate the Bieri--Neumann--Strebel--Renz (BNSR) invariants of irreducible uniform lattices. In the case of a direct product of a tree and a Euclidean space we show that vanishing of the BNSR invariants for all finite-index subgroups of a given uniform lattice is equivalent to irreducibility. On the other hand we construct irreducible uniform lattices which admit maps to the integers whose kernels' finiteness properties are determined by the finiteness properties of certain Bestvina--Brady groups.

arXiv commentv3 final version to appear in Proc. Am. Math. Soc.; v2. Major rewrite fixing an error caught by referee, 15 pages; v1. Partially split off from arXiv:2104.13728 at request of a referee - several new results also included, 18 pages