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