Profinite properties of graph manifolds

By Henry Wilton, Pavel A. Zalesskii. 2008

72 citations recorded by the source corpus.

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. We go on to prove that π1(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 π1(M) is conjugacy separable.

Subfields: Computer Graphics and Computer-Aided Design, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dc3f23d72e97dac4f7f3b4827dbef36d089f793b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Graphics and Computer-Aided Design

1. Gareth Wilkes
2. Henry Wilton
3. Pavel A. Zalesskii

In Geometry and Topology

1. Gareth Wilkes
2. Pavel A. Zalesskii
3. Henry Wilton

In Mathematical Physics

1. Gareth Wilkes
2. Pavel A. Zalesskii
3. Henry Wilton

Citations in the corpus

• Profinite rigidity for Seifert fibre spaces (2015, background): “Finally, we can piece together these geometric manifold with a theorem of Wilton and Zalesskii [WZ10], that if all pieces of the JSJ (or prime) decomposition have good fundamental group, so does the whole manifold, to conclude: Theorem (Agol, Wilton-Zalesskii).”
• Acylindrical hyperbolicity of groups acting on trees (2013, unknown): “The following result was proved by Wilton and Zalesskii in [91].”
• Distinguishing geometries using finite quotients (2014, result): “In the nongeometric case, this follows from the results of [19; 48].”