The Michigan Mathematical Journal
- Michigan Math. J.
- Volume 68, Issue 4 (2019), 743-753.
The Alexander Method for Infinite-Type Surfaces
We prove that for any infinite-type orientable surface , there exists a collection of essential curves in 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 , the curve complex of . As a consequence, we obtain that the natural action of the extended mapping class group of on is faithful.
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
Permanent link to this document
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. https://projecteuclid.org/euclid.mmj/1561773633