Profinite properties of graph manifolds

Details Profinite properties of graph manifolds Profinite properties of graph manifolds

2008-07-23

arxiv.org/abs/0807.3727v2

Mathematics

Group Theory

v2, corrected an error in Lemma 2.3. 25 pages

Scientific paper

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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