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arXiv · 0807.3727

Profinite properties of graph manifolds

Henry Wilton·Pavel Zalesskii
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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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Henry Wilton, Pavel Zalesskii. 2012-08-07. Profinite properties of graph manifolds. https://arxiv.org/abs/0807.3727

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