# 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 $M$ .

## 20 Citations

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

- Mathematics
- 2018

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…

### Grothendieck rigidity of 3-manifold groups

- MathematicsGroups, Geometry, and Dynamics
- 2019

We show that fundamental groups of compact, orientable, irreducible 3-manifolds with toroidal boundary are Grothendieck rigid.

### Toward and after virtual specialization in $3$-manifold topology

- MathematicsSurveys in Differential Geometry
- 2020

. This article surveys works in 3 –manifold topology after the proof of the virtual Haken conjecture. It reviews the virtual specialization of 3 –manifold groups, and some following development of…

### Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups

- MathematicsInventiones mathematicae
- 2022

For any orientable finite-volume hyperbolic 3-manifold, this paper proves that the profinite isomorphism type of the fundamental group uniquely determines the isomorphism type of the first integral…

### The profinite completion of accessible groups

- Mathematics
- 2022

We introduce a class A of ﬁnitely generated residually ﬁnite accessible groups with some natural restriction on one-ended vertex groups in their JSJ-decompositions. We prove that the proﬁnite…

### Profinite genus of fundamental groups of torus bundles

- Mathematics
- 2020

Abstract In this article we prove that the profinite genus of the fundamental group of a torus bundle MA is equal to the order of the class group of the number field where λ is an eigenvalue of the…

### Profinite rigidity for twisted Alexander polynomials

- MathematicsJournal für die reine und angewandte Mathematik (Crelles Journal)
- 2020

We formulate and prove a profinite rigidity theorem for the twisted Alexander polynomials up to several types of finite ambiguity. We also establish torsion growth formulas of the twisted homology…

### On the profinite rigidity of surface groups and surface words

- Mathematics
- 2020

Surface groups are determined among limit groups by their profinite completions. As a corollary, the set of surface words in a free group is closed in the profinite topology.

### Relative cohomology theory for profinite groups

- MathematicsJournal of Pure and Applied Algebra
- 2019

### The profinite completions of knot groups determine the Alexander polynomials

- MathematicsAlgebraic & Geometric Topology
- 2018

We study several properties of the completed group ring $\widehat{\mathbb{Z}}[[t^{\widehat{\mathbb{Z}}}]]$ and the completed Alexander modules of knots. Then we prove that if the profinite…

## References

SHOWING 1-10 OF 54 REFERENCES

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

- Mathematics
- 2018

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

- Mathematics
- 2008

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

- MathematicsWhat's Next?
- 2019

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

- Mathematics
- 2015

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

- Mathematics
- 2015

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

- Mathematics
- 2016

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

- MathematicsJ. Lond. Math. Soc.
- 2013

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

- Mathematics
- 2000

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

- Mathematics
- 2014

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…