Separability of double cosets and conjugacy classes in 3-manifold groups
Group Theory
2014-02-26 v2 Geometric Topology
Abstract
Let M = H^3 / \Gamma be a hyperbolic 3-manifold of finite volume. We show that if H and K are abelian subgroups of \Gamma and g is in \Gamma, then the double coset HgK is separable in \Gamma. As a consequence we prove that if M is a closed, orientable, Haken 3-manifold and the fundamental group of every hyperbolic piece of the torus decomposition of M is conjugacy separable then so is the fundamental group of M. Invoking recent work of Agol and Wise, it follows that if M is a compact, orientable 3-manifold then \pi_1(M) is conjugacy separable.
Cite
@article{arxiv.1109.2765,
title = {Separability of double cosets and conjugacy classes in 3-manifold groups},
author = {Emily Hamilton and Henry Wilton and Pavel Zalesskii},
journal= {arXiv preprint arXiv:1109.2765},
year = {2014}
}
Comments
25 pages; incorporates Agol's solution to the Virtually Haken Conjecture to prove conjugacy separability for all 3-manifold groups; to appear in the Journal of the LMS