## 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(F*_{n}) and the Eichler–Shimura
isomorphism

By work of Kontsevich, the rational cohomology of Out(F_{n})
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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