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arxiv: 0807.3727 · v3 · pith:54YD5V2Cnew · submitted 2008-07-23 · 🧮 math.GR

Profinite properties of graph manifolds

classification 🧮 math.GR
keywords provedecompositiongraphmanifoldprofiniteclosedconjugacyefficient
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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.

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