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

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.

Minor revisions from last version; 47 pages, to appear in Invent. Math

References in corpus (1)

• Some 3-manifold groups with the same finite quotients

Cited by in corpus (2)

• Survey on L^2-invariants and 3-manifolds
• Finite quotients, arithmetic invariants, and hyperbolic volume