Oberseminar Deformationsquantisierung und Geometrie: Rosa Marchesini (JMU)

Abstract:

We present explicit formulas for computing cohomology theories associated with transitive Lie algebroids whose base manifold is homotopy equivalent to a product of spheres. Our approach builds on techniques developed in joint work with M. Jotz and is further extended through ongoing collaboration with R. Louis.

These computations give explicit descriptions of central extensions and aim to provide information on the deformation theory of transitive Lie algebroids. Moreover, they serve as a first step toward applying similar methods to compute cohomology theories of non-transitive Lie ($\infty$)-algebroids. These are expected to yield insights into Poisson geometry and singular foliations.