Topology & Geometric Group Theory Seminar

Spring 2010

1:30 – 2:30, Malott 203

Tuesday, March 9

Jim Conant, University of Tennessee

The cohomology of Out(Fn) and the Eichler–Shimura isomorphism

By work of Kontsevich, the rational cohomology of Out(Fn) can be studied via the cohomology of a certain infinite dimensional Lie algebra. The abelianization of this Lie algebra becomes quite useful in extracting cohomological information, and indeed, to this end, Morita made a conjecture about the abelianization many years ago. Recently Kassabov discovered a general method for computing the abelianization, and it turns out that there is much more than what Morita had guessed. I will explain Kassabov's result and show how the Eichler–Shimura isomorphism, which connects the cohomology of SL(2,Z) with modular forms, can be used to establish the next piece of the abelianization beyond Morita's. (Joint work with Martin Kassabov and Karen Vogtmann.)

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