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A Faithful Action of the Mapping Class Group Mod(Sg) on the (2g−1)-Sphere
Abstract
We prove that Mod(Sg) acts faithfully by orientation-preserving homeomorphisms on a (2g−1)-sphere when g ≥ 3 using equivariant blow-up and bi-orderability of the Torelli group.
Related
- Sphere decomposition for finite subgroups of 3-manifold mapping class groups
- Generating the twist subgroup of the level $2$ mapping class group of a non-orientable closed surface
- An explicit section of the Laudenbach-type exact sequence of the big mapping class group of MΓ
- Mapping class group actions on the cohomology of configuration spaces of surfaces
- Infinitely many Nielsen classes in mapping class groups and free-group automorphism groups
BibTeX
@misc{wang2026faithful,
title = {{A Faithful Action of the Mapping Class Group $\mathrmMod(S_g)$ on the $(2g-1)$-Sphere}},
author = {Shile Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10577},
eprint = {2610.10577},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10577},
}
RIS
TY - UNPB
TI - A Faithful Action of the Mapping Class Group Mod(S_g) on the (2g−1)-Sphere
AU - Shile Wang
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.10577
UR - https://arxiv.org/abs/2610.10577
AB - We prove that Mod(S_g) acts faithfully by orientation-preserving homeomorphisms on a (2g−1)-sphere when g ≥ 3 using equivariant blow-up and bi-orderability of the Torelli group.
ER -