Abstract

In two seminal papers in the early 1990's M. Kontsevich defined graph homology, which are homology of differential graded vector spaces generated by certain isomorphism classes of oriented graphs. Via classical invariant theory he showed on one hand that they could be used to calculate Lie algebra homology of several infinite dimensional Lie algebras; and on the other hand related them to such classical things such as homology of moduli spaces of Riemann surfaces, stable homology of Out(F_n), invariants of three manifolds,... In this talk first I give an overview of these results, then present a simpler graph sub-complexes quasi isomorphic to the larger one, and finally if time allows I will point out the relation of these stuff with the homology of the spaces of branch coverings.



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