JournalscmhVol. 86, No. 3pp. 537–556

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

  • Nathan Broaddus

    University of Chicago, USA
  • Benson Farb

    University of Chicago, USA
  • Andrew Putman

    Rice University, Houston, USA
Irreducible Sp-representations and subgroup distortion in the mapping class group cover
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Abstract

We prove that various subgroups of the mapping class group Mod(Σ)\mathrm{Mod}(\Sigma) of a surface Σ\Sigma are at least exponentially distorted. Examples include the Torelli group (answering a question of Hamenstädt), 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 H1(Σ;Z)\mathrm{H}_1(\Sigma;\mathbb{Z}).

Cite this article

Nathan Broaddus, Benson Farb, Andrew Putman, Irreducible Sp-representations and subgroup distortion in the mapping class group. Comment. Math. Helv. 86 (2011), no. 3, pp. 537–556

DOI 10.4171/CMH/233