Finiteness of mapping class groups and Heegaard distance
Geometric Topology
2023-03-07 v1
Abstract
We prove that the mapping class group of a Heegaard splitting with a distance of at least 3 is finite. However, we have constructed a counterexample with a distance of 2 that disproves this assertion. In addition, the fact that the mapping class group of a Heegaard splitting with a distance of at most 1 is infinite, when combined with our results, provides an answer to the question of the finiteness of mapping class groups as viewed from Heegaard distance.
Cite
@article{arxiv.2303.02849,
title = {Finiteness of mapping class groups and Heegaard distance},
author = {Yanqing Zou},
journal= {arXiv preprint arXiv:2303.02849},
year = {2023}
}
Comments
7 Pages. Comments welcome!