JournalsggdVol. 13, No. 4pp. 1373–1399

Big Torelli groups: generation and commensuration

  • Javier Aramayona

    Universidad Autónoma de Madrid, Spain
  • Tyrone Ghaswala

    University of Manitoba, Winnipeg, Canada
  • Autumn E. Kent

    University of Wisconsin at Madison, USA
  • Alan McLeay

    Université de Luxembourg, Luxembourg
  • Jing Tao

    University of Oklahoma, Norman, USA
  • Rebecca R. Winarski

    University of Michigan, Ann Arbor, USA
Big Torelli groups: generation and commensuration cover

A subscription is required to access this article.

Abstract

For any surface Σ\Sigma of infinite topological type, we study the Torelli subgroup I(Σ)\mathcal I(\Sigma) of the mapping class group MCG(Σ)(\Sigma), whose elements are those mapping classes that act trivially on the homology of Σ\Sigma. Our first result asserts that I(Σ){\mathcal I}(\Sigma) is topologically generated by the subgroup of MCG(Σ)(\Sigma) consisting of those elements in the Torelli group which have compact support. Next, we prove the abstract commensurator group of I(Σ){\mathcal I}(\Sigma) coincides with MCG(Σ)(\Sigma). This extends the results for finite-type surfaces [9, 6, 7, 16] to the setting of infinite-type surfaces.

Cite this article

Javier Aramayona, Tyrone Ghaswala, Autumn E. Kent, Alan McLeay, Jing Tao, Rebecca R. Winarski, Big Torelli groups: generation and commensuration. Groups Geom. Dyn. 13 (2019), no. 4, pp. 1373–1399

DOI 10.4171/GGD/526