Oberseminar Deformationsquantisierung und Geometrie: Rosa Marchesini (Göttingen)

Abstract: Several extensively studied cohomology theories play an important role in differential geometry and mathematical physics. Examples are De Rham cohomology, Chevalley-Eilenberg cohomology, BRST cohomology, and then Poisson, Foliated, and Principal de Rham cohomologies. These are all special cases of Lie algebroid cohomology. 

After an accessible introduction to Lie algebroid cohomology, we propose a notion of homotopy for Lie algebroids and justify it with examples and applications. This is a joint work with Madeleine Jotz.

Special attention is given to the case of Poisson manifolds and Poisson cohomology, which is currently in progress. Other ongoing and future research directions are mentioned.