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Let  M =ℍ 3 /Γ be a hyperbolic 3‐manifold of finite volume. We show that if  H  and  K  are abelian subgroups of Γ and  g ∈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.

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