## The Michigan Mathematical Journal

### The Alexander Method for Infinite-Type Surfaces

#### 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 an infinite complement in $\mathcal{C}(S)$, the curve complex of $S$. As a consequence, we obtain that the natural action of the extended mapping class group of $S$ on $\mathcal{C}(S)$ is faithful.

#### Article information

Source
Michigan Math. J., Volume 68, Issue 4 (2019), 743-753.

Dates
Revised: 24 May 2018
First available in Project Euclid: 29 June 2019

https://projecteuclid.org/euclid.mmj/1561773633

Digital Object Identifier
doi:10.1307/mmj/1561773633

Subjects

#### Citation

Hernández Hernández, Jesús; Morales, Israel; Valdez, Ferrán. The Alexander Method for Infinite-Type Surfaces. Michigan Math. J. 68 (2019), no. 4, 743--753. doi:10.1307/mmj/1561773633. https://projecteuclid.org/euclid.mmj/1561773633

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