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L’Enseignement Mathématique

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Volume 58, Issue 1/2, 2012, pp. 165–188
DOI: 10.4171/LEM/58-1-8

Published online: 2012-06-30

Generating the Torelli group

Allen Hatcher[1] and Dan Margalit[2]

(1) Cornell University, Ithaca, USA
(2) 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~$3$ is generated by simple homeomorphisms known as {\it 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.

Keywords: Torelli group, bounding pair maps

Hatcher Allen, Margalit Dan: Generating the Torelli group. Enseign. Math. 58 (2012), 165-188. doi: 10.4171/LEM/58-1-8