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Sphere decomposition for finite subgroups of 3-manifold mapping class groups
Abstract
For a closed, oriented 3-manifold M, we show that any finite subgroup of its mapping class group preserves an isotopy class of filling sphere system on M. This is an isotopy version of the "equivariant sphere theorem" of Meeks-Yau. As part of our analysis, we establish a bijection between simplices of the Guirardel--Levitt outer space for π1(M) and filling sphere systems in M, generalizing an argument of Hatcher. We also compute the image of Homeo(M)→Out(π1M) for any such M.
Related
- Hopf decomposition of the actions of subgroups of the mapping class group
- Ivanov's finite-index Frattini conjecture for subgroups of mapping class groups
- The Nash manifold of four-point configurations modulo similarity subgroups
- An irreducible decomposition of the Weil representation restricted to open compact subgroups
- Gallai Decomposition of Ordered Groups: Subgroups, Quotients, and the N-free Case
BibTeX
@misc{bregman2026sphere,
title = {{Sphere decomposition for finite subgroups of 3-manifold mapping class groups}},
author = {Corey Bregman and Bena Tshishiku},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31798},
eprint = {2610.31798},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31798},
}
RIS
TY - UNPB
TI - Sphere decomposition for finite subgroups of 3-manifold mapping class groups
AU - Corey Bregman
AU - Bena Tshishiku
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31798
UR - https://arxiv.org/abs/2610.31798
AB - For a closed, oriented 3-manifold M, we show that any finite subgroup of its mapping class group preserves an isotopy class of filling sphere system on M. This is an isotopy version of the "equivariant sphere theorem" of Meeks-Yau. As part of our analysis, we establish a bijection between simplices of the Guirardel--Levitt outer space for π_1(M) and filling sphere systems in M, generalizing an argument of Hatcher. We also compute the image of Homeo(M)→Out(π_1M) for any such M.
ER -