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

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

2007-07-16

arxiv.org/abs/0707.2262v3

Mathematics

Geometric Topology

17 pages; a few corrections; to appear in Comment. Math. Helv

Scientific paper

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 Hamenst\"adt), 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 $\HH_1(\Sigma;\Z)$.

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