PreprintCC BY 4.0arXiv
A survey on mapping class groups of 3-manifolds
Abstract
We survey computations and tools concerning the mapping class group of a compact, oriented, connected 3-manifold M. We provide a guide to the literature and sketch proofs for various families of irreducible and geometric 3-manifolds. We also consider JSJ and prime decompositions of 3-manifolds, and consequences for their mapping class groups.
Related
- On the mapping class groups of simply connected smooth 4-manifolds
- Mapping class groups of negatively curved four-manifolds
- Mapping class groups of solenoidal manifolds
- Topological mapping class groups of non-simply connected 4-manifolds
- Mapping class groups of simply connected closed spin 5-manifolds with no 2- and 3-torsion in homology
BibTeX
@misc{bader2026survey,
title = {{A survey on mapping class groups of 3-manifolds}},
author = {Philipp Bader and Rachael Boyd and Giulia Carfora and Gabriel Corrigan and Daniel Galvin and Csaba Nagy and John Nicholson and Weizhe Niu and Isacco Nonino and Mark Pencovitch and Mark Powell},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00233},
eprint = {2609.00233},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00233},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A survey on mapping class groups of 3-manifolds
AU - Philipp Bader
AU - Rachael Boyd
AU - Giulia Carfora
AU - Gabriel Corrigan
AU - Daniel Galvin
AU - Csaba Nagy
AU - John Nicholson
AU - Weizhe Niu
AU - Isacco Nonino
AU - Mark Pencovitch
AU - Mark Powell
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00233
UR - https://arxiv.org/abs/2609.00233
AB - We survey computations and tools concerning the mapping class group of a compact, oriented, connected 3-manifold M. We provide a guide to the literature and sketch proofs for various families of irreducible and geometric 3-manifolds. We also consider JSJ and prime decompositions of 3-manifolds, and consequences for their mapping class groups.
ER -