High dimensional hyperbolic Coxeter groups that virtually fiber

TL;DR

This paper introduces an iterative method to construct hyperbolic Coxeter groups that virtually fiber over the integers, producing infinitely many distinct groups across all virtual cohomological dimensions.

Contribution

It combines existing results with a new thickening process to generate a broad class of hyperbolic Coxeter groups with controlled virtual cohomological dimensions.

Findings

Produces infinitely many isomorphism classes in each vcd ≥ 2

Ensures vcd increases by exactly one with each iteration

Constructs examples for every virtual cohomological dimension

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) $n\geq 2$. 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.