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Surface group amalgams that (don't) act on 3-manifolds

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arxiv 1705.01361 v2 pith:RZ5WT4GP submitted 2017-05-03 math.GT math.GR

G. Christopher Hruska , Emily Stark , Hung Cong Tran This is my paper · ORCID
classification math.GTmath.GR
keywords surfacegroupgroupsamalgamamalgamscoxeterdeterminefundamental
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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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  1. Subgroups of right-angled Coxeter groups via Stallings-like techniques

    math.GT 2019-08 conditional novelty 8.0 of 10

    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.

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