Surface group amalgams that (don't) act on 3-manifolds
Geometric Topology
2018-09-05 v2 Group Theory
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.
Keywords
Cite
@article{arxiv.1705.01361,
title = {Surface group amalgams that (don't) act on 3-manifolds},
author = {G. Christopher Hruska and Emily Stark and Hung Cong Tran},
journal= {arXiv preprint arXiv:1705.01361},
year = {2018}
}
Comments
v2: 30 pages, 10 figures; minor changes. To appear in American Journal of Mathematics