Generating the Torelli group
Allen Hatcher
Cornell University, Ithaca, USADan Margalit
Georgia Institute of Technology, Atlanta, United States
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Abstract
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