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Generating the Torelli group

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.

preprint2012arXivOpen access
Allen HatcherDan Margalit
math.GRmath.GT
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Allen HatcherDan Margalit

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