Virtually Fibering Right-Angled Coxeter Groups

Abstract

We show that certain right-angled Coxeter groups have finite index subgroups that quotient to $\mathbb{Z}$ with finitely generated kernels. The proof uses Bestvina-Brady Morse theory facilitated by combinatorial arguments. We describe a variety of examples where the plan succeeds or fails. Among the successful examples are the right-angled reflection groups in ${\mathbb{H}}^4$ with fundamental domain the $120$-cell or the $24$-cell.

30 pages, to appear in J. Inst. Math. Jussieu

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