Profinite properties of graph manifolds

Abstract

Let M be a closed, orientable, irreducible, geometrizable 3-manifold. We prove that the profinite topology on the fundamental group of π_1(M) is efficient with respect to the JSJ decomposition of M. We go on to prove that π_1(M) is good, in the sense of Serre, if all the pieces of the JSJ decomposition are. We also prove that if M is a graph manifold then π_1(M) is conjugacy separable.

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