High dimensional hyperbolic Coxeter groups that virtually fiber

Abstract

This paper provides an iterative procedure for constructing hyperbolic Coxeter groups that virtually fiber over $\mathbb{Z}$ that is flexible enough to yield infinitely many isomorphism classes in each virtual cohomological dimension (vcd) $n\ge 2$. Our procedure combines results of Jankiewicz, Norin, and Wise with a generalization of a construction due to Osajda involving a new simplicial thickening process. We also give a topological argument showing that the vcd of the right-angled Coxeter groups produced by our construction increases by exactly one with each iteration, guaranteeing that our process produces examples of every vcd.

Minor corrections and edits. To appear in Math. Ann