Automorphisms of the Torelli complex and the complex of separating curves

Details Automorphisms of the Torelli complex and the complex of separating curves Automorphisms of the Torelli complex and the complex of separating curves

2009-09-25

arxiv.org/abs/0909.4718v3

J.Math.Soc.Japan 63 (2011) 363-417

Mathematics

Group Theory

43 pages, 12 figures

Scientific paper

10.2969/jmsj/06320363

We compute the automorphism groups of the Torelli complex and the complex of
separating curves for all but finitely many compact orientable surfaces. As an
application, we show that the abstract commensurators of the Torelli group and
the Johnson kernel for such surfaces are naturally isomorphic to the extended
mapping class group.

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