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November 2019 The Alexander Method for Infinite-Type Surfaces
Jesús Hernández Hernández, Israel Morales, Ferrán Valdez
Michigan Math. J. 68(4): 743-753 (November 2019). DOI: 10.1307/mmj/1561773633

Abstract

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.

Citation

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Jesús Hernández Hernández. Israel Morales. Ferrán Valdez. "The Alexander Method for Infinite-Type Surfaces." Michigan Math. J. 68 (4) 743 - 753, November 2019. https://doi.org/10.1307/mmj/1561773633

Information

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

zbMATH: 07155047
MathSciNet: MR4029627
Digital Object Identifier: 10.1307/mmj/1561773633

Subjects:
Primary: 20F65

Rights: Copyright © 2019 The University of Michigan

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Vol.68 • No. 4 • November 2019
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