Back to Search
Start Over
Finite quotients of 3-manifold groups.
- Source :
-
Inventiones Mathematicae . Jul2024, Vol. 237 Issue 1, p349-440. 92p. - Publication Year :
- 2024
-
Abstract
- For G and H 1 , ... , H n finite groups, does there exist a 3-manifold group with G as a quotient but no H i 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FINITE groups
*FUNDAMENTAL groups (Mathematics)
*COHOMOLOGY theory
Subjects
Details
- Language :
- English
- ISSN :
- 00209910
- Volume :
- 237
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Inventiones Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 177797618
- Full Text :
- https://doi.org/10.1007/s00222-024-01262-4