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

Nathan Broaddus; Benson Farb; Andrew Putman

doi:10.4171/CMH/233

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

Geometric Topology 2020-06-11 v4 Group Theory

Authors: Nathan Broaddus , Benson Farb , Andrew Putman

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

Keywords

torelli group mapping class groups of surfaces mapping class groups

Cite

@article{arxiv.0707.2262,
  title  = {Irreducible Sp-representations and subgroup distortion in the mapping class group},
  author = {Nathan Broaddus and Benson Farb and Andrew Putman},
  journal= {arXiv preprint arXiv:0707.2262},
  year   = {2020}
}

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

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

Abstract

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