English

Non-realizability of some big mapping class groups

Geometric Topology 2022-09-07 v2 Group Theory

Abstract

In this note, we prove that the compactly supported mapping class group of a surface containing a genus 33 subsurface has no realization as a subgroup of the homeomorphism group. We also prove that for certain surfaces with order 66 symmetries, their mapping class groups have no realization as a subgroup of the homeomorphism group. Examples of such surfaces include the plane minus a Cantor set and the sphere minus a Cantor set.

Keywords

Cite

@article{arxiv.2111.08583,
  title  = {Non-realizability of some big mapping class groups},
  author = {Lei Chen and Yan Mary He},
  journal= {arXiv preprint arXiv:2111.08583},
  year   = {2022}
}

Comments

The updated version contains new theorems

R2 v1 2026-06-24T07:40:53.237Z