Irreducible Sp-representations and subgroup distortion in the mapping class group
Nathan Broaddus
University of Chicago, USABenson Farb
University of Chicago, USAAndrew Putman
Rice University, Houston, USA
![Irreducible Sp-representations and subgroup distortion in the mapping class group cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserials%2Fcover-cmh.png&w=3840&q=90)
Abstract
We prove that various subgroups of the mapping class group of a surface 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 .
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