Alexander A. Voronov
University of Minnesota
Graph Homology: Koszul and Verdier Duality
Abstract: The popularity of graph homology owes largely to the fact
that the cohomology of two important groups in mathematics, the outer
automorphism group of a free group and the mapping class group, even
though generally incomputable, may be computed via a deceptively
simple combinatorial construction, called graph homology. Such
computations, done by Culler-Vogtmann, Penner, and Kontsevich indicate
that, in certain particular cases, Poincare-type duality on the level
of spaces corresponds to Koszul duality of operads. In this talk,
based on a joint work with Andrey Lazarev, we explain how Verdier
duality on graph spaces turns into Koszul duality for operads, in
general.