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arXiv · 1703.00407

The Alexander method for infinite-type surfaces

Jesus Hernandez Hernandez·Israel Morales·Ferran Valdez
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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 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.

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Jesus Hernandez Hernandez, Israel Morales, Ferran Valdez. 2017-03-01. The Alexander method for infinite-type surfaces. https://arxiv.org/abs/1703.00407

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