Separability of double cosets and conjugacy classes in 3-manifold groups

Abstract

Let M = H^3 / Γbe a hyperbolic 3-manifold of finite volume. We show that if H and K are abelian subgroups of Γand g is in Γ, then the double coset HgK is separable in Γ. 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 π_1(M) is conjugacy separable.

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

References in corpus (1)

• Residual finiteness, QCERF, and fillings of hyperbolic groups

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