Finite quotients of 3-manifold groups

Will Sawin, Melanie Matchett Wood

Research output: Contribution to journalArticlepeer-review


For G and H1,…,Hn finite groups, does there exist a 3-manifold group with G as a quotient but no Hi as a quotient? We answer all such questions in terms of the group cohomology of finite groups. We prove non-existence with topological results generalizing the theory of semicharacteristics. To prove existence of 3-manifolds with certain finite quotients but not others, we use a probabilistic method, by first proving a formula for the distribution of the (profinite completion of) the fundamental group of a random 3-manifold in the Dunfield-Thurston model of random Heegaard splittings as the genus goes to infinity. We believe this is the first construction of a new distribution of random groups from its moments.

Original languageEnglish (US)
Pages (from-to)349-440
Number of pages92
JournalInventiones Mathematicae
Issue number1
StatePublished - Jul 2024

All Science Journal Classification (ASJC) codes

  • General Mathematics


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