Generating the Torelli group

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 3 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.

23 pages, 10 figures, improvements to the exposition, to appear in L'Enseignement Mathematique

References in corpus (1)

• A note on the connectivity of certain complexes associated to surfaces

Cited by in corpus (3)

• The Torelli group and congruence subgroups of the mapping class group
• The Johnson homomorphism and its kernel
• Cohomology of the hyperelliptic Torelli group