Alexander Berglund: Lie algebras of symplectic derivations and graph complexes

Abstract: I will present a simple proof of a theorem of Kontsevich, which states that the symplectic invariants in the Chevalley-Eilenberg complex of the Lie algebra of symplectic derivations on a free Lie algebra is isomorphic to the graph complex that computes the cohomology of outer automorphism groups of free groups. The main ingredients of the proof are classical invariant theory (specifically the description of symplectic invariants in tensor powers of a symplectic vector space) and an elementary lemma about colimits over Grothendieck constructions.