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

Abstract

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 $H_1(\Sigma ;\mathbb{Z})$.

17 pages; fixed TeX errors in arXiv title and abstract, paper unchanged

Cited by in corpus (11)

• The Picard group of the moduli space of curves with level structures
• The Torelli group and congruence subgroups of the mapping class group
• Lagrangian mapping class groups from a group homological point of view
• A Birman exact sequence for Aut(F_n)
• The abelianization of the level L mapping class group
• A minimal generating set of the level 2 mapping class group of a non-orientable surface
• Affine diffeomorphism groups are undistorted
• The Dehn function of Sp(2n;Z)
• Partial Torelli groups and homological stability
• The action of mapping class groups on de Rham quasimorphisms
• Two mod-p Johnson filtrations