Profinite detection of 3-manifold decompositions

@article{Wilton2019ProfiniteDO,
  title={Profinite detection of 3-manifold decompositions},
  author={Henry Wilton and Pavel Zalesskii},
  journal={Compositio Mathematica},
  year={2019},
  volume={155},
  pages={246 - 259}
}
The profinite completion of the fundamental group of a closed, orientable $3$ -manifold determines the Kneser–Milnor decomposition. If $M$ is irreducible, then the profinite completion determines the Jaco–Shalen–Johannson decomposition of $M$ . 

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References

SHOWING 1-10 OF 54 REFERENCES

Profinite completions, cohomology and JSJ decompositions of compact 3-manifolds

In this paper we extend previous results concerning the behaviour of JSJ decompositions of closed 3-manifolds with respect to the profinite completion to the case of compact 3-manifolds with

Profinite properties of graph manifolds

Let M be a closed, orientable, irreducible, geometrizable 3-manifold. We prove that the profinite topology on the fundamental group of π1(M) is efficient with respect to the JSJ decomposition of M.

The Profinite Completion of 3-Manifold Groups, Fiberedness and the Thurston Norm

We show that a regular isomorphism of profinite completion of the fundamental groups of two 3-manifolds $N_1$ and $N_2$ induces an isometry of the Thurston norms and a bijection between the fibered

Profinite rigidity for Seifert fibre spaces

An interesting question is whether two 3-manifolds can be distinguished by computing and comparing their collections of finite covers; more precisely, by the profinite completions of their

3-Manifold Groups

We summarize properties of 3-manifold groups, with a particular focus on the consequences of the recent results of Ian Agol, Jeremy Kahn, Vladimir Markovic and Dani Wise.

Profinite rigidity and surface bundles over the circle

If M is a compact 3‐manifold whose first betti number is 1, and N is a compact 3‐manifold such that π1N and π1M have the same finite quotients, then M fibres over the circle if and only if N does. We

Separability of double cosets and conjugacy classes in 3‐manifold groups

TLDR
It is proved that if M is a closed, orientable, Haken 3-manifold and the fundamental group of every hyperbolic piece of the torus decomposition of M is conjugacy separable then so is the Fundamental group of M.

Bounds on exceptional Dehn filling

We show that for a hyperbolic knot complement, all but at most 12 Dehn llings are irreducible with innite word-hyperbolic fundamental group.

Some 3-manifold groups with the same finite quotients

We give examples of closed, oriented 3-manifolds whose fundamental groups are not isomorphic, but yet have the same sets of finite quotient groups; hence the same profinite completions. We also give
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