The number of ends of big mapping class groups
Geometric Topology
2025-12-19 v2 Group Theory
Metric Geometry
Abstract
We analyze the number of ends of the mapping class group of a stable avenue surface. We prove that the mapping class group is one-ended whenever the stable avenue surface has at least one end of discrete type. Our method is to show that the associated translatable curve graph, which is quasi-isometric to the mapping class group, is one-ended.
Cite
@article{arxiv.2512.09776,
title = {The number of ends of big mapping class groups},
author = {Josiah Oh and Yulan Qing and Xiaolei Wu},
journal= {arXiv preprint arXiv:2512.09776},
year = {2025}
}