Irreducible Sp-representations and subgroup distortion in the mapping class group

Nathan Broaddus, Benson Farb, Andrew Putman
Arxiv ID: 0707.2262Last updated: 6/11/2020
We prove that various subgroups of the mapping class group $Mod(\Sigma)$ of a surface $\Sigma$ are at least exponentially distorted. Examples include the Torelli group (answering a question of Hamenstadt), the "point-pushing" and surface braid subgroups, and the Lagrangian subgroup. Our techniques include a method to compute lower bounds on distortion via representation theory and an extension of Johnson theory to arbitrary subgroups of $H_1(\Sigma;\mathbb{Z})$.

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