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 ${\pi }_1(M)$ is efficient with respect to the JSJ decomposition of $M$. We go on to prove that ${\pi }_1(M)$ 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 ${\pi }_1(M)$ is conjugacy separable.

v2, corrected an error in Lemma 2.3. v3 filled a gap in the proof (see Definition 5.1). 26 pages

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