Unicorn paths and hyperfiniteness for the mapping class group
Keyword(s):
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 Hamenstädt and Kida that this action is universally amenable and that the mapping class group of S is exact.
Keyword(s):
2016 ◽
Vol 25
(05)
◽
pp. 1650022
2018 ◽
Vol 2020
(24)
◽
pp. 9974-9987
Keyword(s):