The Alexander method for infinite-type surfaces
Geometric Topology
2017-03-02 v1
Abstract
We prove that for any infinite-type orientable surface S there exists a collection of essential curves {\Gamma} in S such that any homeomorphism that preserves the isotopy classes of the elements of {\Gamma} is isotopic to the identity. The collection {\Gamma} is countable and has infinite complement in C(S), the curve complex of S. As a consequence we obtain that the natural action of the extended mapping class group of S on C(S) is faithful.
Keywords
Cite
@article{arxiv.1703.00407,
title = {The Alexander method for infinite-type surfaces},
author = {Jesus Hernandez Hernandez and Israel Morales and Ferran Valdez},
journal= {arXiv preprint arXiv:1703.00407},
year = {2017}
}
Comments
11 pages, 5 figures