The Michigan Mathematical Journal

The Alexander Method for Infinite-Type Surfaces

Jesús Hernández Hernández, Israel Morales, and Ferrán Valdez

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

Article information

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

Received: 20 September 2017
Revised: 24 May 2018
First available in Project Euclid: 29 June 2019

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Digital Object Identifier

Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]


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.

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