Profinite properties of graph manifolds

2008/07/23 by Henry Wilton, Wilton, Henry, Pavel Zalesskii +1 · 1 citation
Computer Science · Mathematics · #20E26 #57N10 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.0807.3727

openalex publication_date 2008/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Toward the profinite rigidity of hyperbolic 3-manifolds
• On regularity of profinite isomorphisms between cusped hyperbolic 3-manifolds and the A-polynomial

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