Profinite properties of graph manifolds

Henry Wilton; Pavel Zalesskii

Profinite properties of graph manifolds

Group Theory 2012-08-08 v3

Authors: Henry Wilton , Pavel Zalesskii

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.

Keywords

manifolds surfaces and embeddings

Cite

@article{arxiv.0807.3727,
  title  = {Profinite properties of graph manifolds},
  author = {Henry Wilton and Pavel Zalesskii},
  journal= {arXiv preprint arXiv:0807.3727},
  year   = {2012}
}

Comments

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

Profinite properties of graph manifolds

Abstract

Keywords

Cite

Comments

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