Type: Article

The Alexander method for infinite-type surfaces

Hernández-Hernández, Jesús; Morales, Israel, Valdez, Ferran;

Abstract:

We prove that for any infinite-type orientable surface S, there exists a collection of essential curves ? in S such that any homeomorphism that preserves the isotopy classes of the elements of ? is isotopic to the identity. The collection ? is countable and has an 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.