English

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.

Keywords

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!

R2 v1 2026-06-28T09:02:35.082Z