Generating the Torelli group

  • Allen Hatcher

    Cornell University, Ithaca, USA
  • Dan Margalit

    Georgia Institute of Technology, Atlanta, United States


We give a new proof of the theorem of Birman–Powell that the Torelli subgroup of the mapping class group of a closed orientable surface of genus at least is generated by simple homeomorphisms known as bounding pair maps. The key ingredient is a proof that the subcomplex of the curve complex of the surface spanned by curves within a fixed homology class is connected.

Cite this article

Allen Hatcher, Dan Margalit, Generating the Torelli group. Enseign. Math. 58 (2012), no. 1/2, pp. 165–188

DOI 10.4171/LEM/58-1-8