Oberseminar Topologie - Prof. James Conant (University of Tennessee): Abelianizing Lie algebras of derivations, and the homology of Out (Fn ).
Monday, 08.11.2010 14:00 im Raum SR 5
Abstract: In this talk we will review a theorem of Kontsevich relating the
homology of a certain Lie algebra of derivations and the rational homology
of Out(F_n). By studying the abelianization of this Lie algebra, Morita was
able to gain a lot of information about the homology of Out(F_n). Morita
found a large piece of the abelianization, but it turns out that there is a
lot more. In joint work with Martin Kassabov and Karen Vogtmann, we show how
to compute all of the abelianization, as an infinite graded vector space.
The first degree corresponds to the part Morita discovered. In degree 2, we
show that the abelianization is put together from spaces of modular forms.
Although degree 3 is known to be highly nontrivial, we do not yet have a
complete characterization.
Angelegt am 25.10.2010 von N. N
Geändert am 08.11.2010 von N. N
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