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

Author： Hamilton Emily   Wilton Henry   Zalesskii Pavel A.  

Publisher： Oxford University Press

ISSN： 0024-6107

Source： Journal of the London Mathematical Society, Vol.87, Iss.1, 2013-02, pp. : 269-288

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Abstract

Let M3/ be a hyperbolic 3-manifold of finite volume. We show that if H and K are abelian subgroups of and g, then the double coset HgK is separable in . 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 1(M) is conjugacy separable.

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