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

2017/05/03 by Hruska, G. Christopher, Stark, Emily, Tran, Hung Cong · 1 citation
#20F65 #20F67 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1705.01361

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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• Cyclic orders and actions of Leary--Minasyan groups on coarse PD(n) spaces

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