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arXiv · 2012.01310

Most big mapping class groups fail the Tits Alternative

Daniel Allcock
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Abstract

Let $X$ be a surface, possibly with boundary. Suppose it has infinite genus or infinitely many punctures, or a closed subset which is a disk with a Cantor set removed from its interior. For example, $X$ could be any surface of infinite type with only finitely many boundary components. We prove that the mapping class group of $X$ does not satisfy the Tits Alternative. That is, Map$(X)$ contains a finitely generated subgroup that is not virtually solvable and contains no nonabelian free group.

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Daniel Allcock. 2020-12-02. Most big mapping class groups fail the Tits Alternative. https://doi.org/10.2140/agt.2021.21.3675

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