Distortion and Tits alternative in smooth mapping class groups

Hurtado, Sebastian; Militon, Emmanuel

doi:10.1090/tran/7476

Distortion and Tits alternative in smooth mapping class groups
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by Sebastian Hurtado and Emmanuel Militon PDF

Trans. Amer. Math. Soc. 371 (2019), 8587-8623

Abstract:

In this article, we study the smooth mapping class group of a surface $S$ relative to a given Cantor set, that is, the group of isotopy classes of orientation-preserving smooth diffeomorphisms of $S$ which preserve this Cantor set. When the Cantor set is the standard ternary Cantor set, we prove that this group does not contain any distorted element. Moreover, we prove a weak Tits alternative for these groups.

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