A subgroup of a right-angled Coxeter group is quasiconvex exactly when its constructed completion complex is finite, and this yields new algorithmic tests for subgroup properties and finite-index embeddability.
Surface group amalgams that (don't) act on 3-manifolds
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abstract
We determine which amalgamated products of surface groups identified over multiples of simple closed curves are not fundamental groups of 3-manifolds. We prove each surface amalgam considered is virtually the fundamental group of a 3-manifold. We prove that each such surface group amalgam is abstractly commensurable to a right-angled Coxeter group from a related family. In an appendix, we determine the quasi-isometry classes among these surface amalgams and their related right-angled Coxeter groups.
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math.GT 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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Subgroups of right-angled Coxeter groups via Stallings-like techniques
A subgroup of a right-angled Coxeter group is quasiconvex exactly when its constructed completion complex is finite, and this yields new algorithmic tests for subgroup properties and finite-index embeddability.