Subgroups of right-angled Coxeter groups via Stallings-like techniques

Pallavi Dani; Ivan Levcovitz

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arXiv · 1908.09046

Subgroups of right-angled Coxeter groups via Stallings-like techniques

Pallavi Dani·Ivan Levcovitz

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Abstract

We associate cube complexes called completions to each subgroup of a right-angled Coxeter group (RACG). A completion characterizes many properties of the subgroup such as whether it is quasiconvex, normal, finite-index or torsion-free. We use completions to show that reflection subgroups are quasiconvex, as are one-ended Coxeter subgroups of a 2-dimensional RACG. We provide an algorithm that determines whether a given one-ended, 2-dimensional RACG is isomorphic to some finite-index subgroup of another given RACG. In addition, we answer several algorithmic questions regarding quasiconvex subgroups. Finally, we give a new proof of Haglund's result that quasiconvex subgroups of RACGs are separable.

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BibTeX RIS

Pallavi Dani, Ivan Levcovitz. 2021-04-13. Subgroups of right-angled Coxeter groups via Stallings-like techniques. https://arxiv.org/abs/1908.09046

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