Automorphisms of Torelli groups

Details Automorphisms of Torelli groups Automorphisms of Torelli groups

2003-11-14

arxiv.org/abs/math/0311250v1

Mathematics

Geometric Topology

Scientific paper

In this paper, we prove that each automorphism of the Torelli group of a surface is induced by a diffeomorphism of the surface, provided that the surface is a closed, connected, orientable surface of genus at least 3. This result was previously announced by Benson Farb for genus at least 4 and has recently been announced by Benson Farb and Nikolai Ivanov for subgroups of finite index in the Torelli group for surfaces of genus at least 5. This result is also directly analogous to previous results established for classical braid groups, mapping class groups, and surface braid groups.

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