Automorphisms of free groups, hairy graphs and modular forms

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• Karen Vogtmann (Cornell)
• Tuesday 07 February 2012, 17:00-18:00
• MR15.

If you have a question about this talk, please contact Christopher Brookes.

The group  of outer automorphisms of a free group  acts on a space of finite graphs known as Outer space, and a classical theorem of Hurwicz implies that the homology of the quotient space is an invariant of the group. Kontsevich related the homology of this quotient to the Lie algebra cohomology of a certain infinite-dimensional symplectic Lie algebra.  Using this connection, S. Morita discovered a series of new homology classes for Out(F_n).  We reinterpret Morita’s classes in terms of hairy graphs, and show how this leads to the construction of large numbers of new classes, including some based on classical modular forms for SL(2,Z). (joint work with J. Conant and M. Kassabov).

This talk is part of the Algebra and Representation Theory Seminar series.

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