Algebra/Topology seminar

Speaker: Rosa Marchesini

Title: An invitation to Lie algebroid cohomology.

Abstract: Several extensively studied cohomology theories play an important role in differential geometry. Examples are De Rham cohomology, Chevalley-Eilenberg cohomology in Lie theory, BRST cohomology in quantum physics, and then Poisson, Foliated, and Principal de Rham cohomologies. All of these can be elegantly formalized at once using special smooth vector bundles called Lie algebroids, which have been studied for decades in higher Lie theory.
After an accessible introduction to Lie algebroids and their cohomology, a notion of homotopy for Lie algebroids is proposed. This leads to a Poincaré lemma and, together with Mayer-Vietoris, to a Künneth formula.
This is a joint work with my supervisor M. Jotz.