Generating the Torelli group
Summary: We give a new proof of the theorem of Birman-Powell that the Torelli subgroup of the mapping classgroup 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.
scientific article; zbMATH DE number 6187662