Generating the Torelli group

Details Generating the Torelli group Generating the Torelli group

2011-10-05

arxiv.org/abs/1110.0876v2

Mathematics

Geometric Topology

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

Scientific paper

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.

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