Arbitrarily high dimensional hyperbolic right-angled Coxeter groups that virtually fiber

A group is said to virtually fiber if it has a finite index subgroup that surjects onto $\mathbb Z$ with a finitely generated kernel. In this talk, we give an iterative procedure that produces infinitely many isomorphism classes of hyperbolic right-angled Coxeter groups (RACGs) in arbitrarily high virtual cohomological dimension $> 2$ that virtually fiber. Our methods involve a novel generalization of a simplicial thickening construction introduced by Osajda (to produce hyperbolic RACGs with arbitrarily high vcd) which allows us to then apply a combinatorial criterion given by Jankiewicz, Norin, Wise that implies virtual fibering of RACGs.

This is joint work with Jean-Francois Lafont, Matthew Stover, Barry Minemyer, and Joseph Wells.