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 subsurface has no realization as a subgroup of the homeomorphism group. We also prove that for certain surfaces with order 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.
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