Virtually Fibering Right-Angled Coxeter Groups

Daniel T. Wise; Kasia Jankiewicz; Sergey Norin

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Virtually Fibering Right-Angled Coxeter Groups

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arxiv 1711.11505 v1 pith:TSVM3ZF5 submitted 2017-11-30 math.GR

Kasia Jankiewicz , Sergey Norin , Daniel T. Wise This is my paper · ORCID

classification math.GR

keywords groupsright-angledcellcoxeterexamplesmathbbargumentsbestvina-brady

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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.

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