Unicorn paths and hyperfiniteness for the mapping class group
Geometric Topology
2021-07-01 v2 Logic
Abstract
Let S be an orientable surface of finite type. Using Pho-On's infinite unicorn paths, we prove the hyperfiniteness of orbit equivalence relations induced by the actions of the mapping class group of S on the Gromov boundaries of the arc graph and the curve graph of S. In the curve graph case, this strengthens the results of Hamenst\"adt and Kida that this action is universally amenable and that the mapping class group of S is exact.
Cite
@article{arxiv.2006.08872,
title = {Unicorn paths and hyperfiniteness for the mapping class group},
author = {Piotr Przytycki and Marcin Sabok},
journal= {arXiv preprint arXiv:2006.08872},
year = {2021}
}
Comments
14 pages, 2 figures