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

@article{Broaddus2007IrreducibleA,
  title={Irreducible \$\Sp\$-representations and subgroup distortion in the mapping class group},
  author={N. Broaddus and B. Farb and A. Putman},
  journal={arXiv: Geometric Topology},
  year={2007}
}
  • N. Broaddus, B. Farb, A. Putman
  • Published 2007
  • Mathematics
  • arXiv: Geometric Topology
  • 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 $\HH_1(\Sigma;\Z)$. 
    28 Citations

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