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

2020/11/18 by Liu, Yi · 4 citations
#30F40 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Primary 57M50 #Secondary 57M10

paper · doi:10.48550/arxiv.2011.09412

Abstract

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 cohomology, as marked with the Thurston norm and the fibered classes; moreover, up to finite ambiguity, the profinite isomorphism type determines the isomorphism type of the fundamental group, among the class of finitely generated 3-manifold groups.

Cited by

• Turaev--Viro invariants and profinite completions of surface bundles
• Toward the profinite rigidity of hyperbolic 3-manifolds
• On regularity of profinite isomorphisms between cusped hyperbolic 3-manifolds and the A-polynomial
• Finite covers and strict boundary slopes of cusped hyperbolic 3-manifolds

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• Absolute profinite rigidity of some closed fibered hyperbolic 3-manifolds
• Countable groups are mapping class groups of hyperbolic 3-manifolds
• Hyperbolic three-manifolds with trivial finite type invariants
• The profinite completion of 3-manifold groups, fiberedness and the Thurston norm
• Toward the profinite rigidity of hyperbolic 3-manifolds