Asymptotic Dimension of Big Mapping Class Groups
Geometric Topology
2021-10-08 v1 Group Theory
Abstract
Even though big mapping class groups are not countably generated, certain big mapping class groups can be generated by a coarsely bounded set and have a well defined quasi-isometry type. We show that the big mapping class group of a stable surface of infinite type with a coarsely bounded generating set that contains an essential shift has infinite asymptotic dimension. This is in contrast with the mapping class groups of surfaces of finite type where the asymptotic dimension is always finite. We also give a topological characterization of essential shifts.
Cite
@article{arxiv.2110.03087,
title = {Asymptotic Dimension of Big Mapping Class Groups},
author = {Curtis Grant and Kasra Rafi and Yvon Verberne},
journal= {arXiv preprint arXiv:2110.03087},
year = {2021}
}
Comments
26 pages, 10 figures