On the homotopy invariance of Lie algebroid cohomology

28.05.2024, 11:00 Uhr (exceptionally)  –  Campus Golm, Building 9, Room 0.13 and via Zoom
Arbeitsgruppenseminar Analysis

Rosa Marchesini (Göttingen)

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. All of these can be elegantly formalized at once using special smooth vector bundles called Lie algebroids. Lie algebroids also arise naturally as an infinitesimal description of Lie groupoids and are therefore a central subject of study in higher Lie theory.
     After an accessible introduction to Lie algebroids and their cohomology, we propose a notion of homotopy for Lie algebroids and justify it with examples and applications. This is a joint work with my supervisor Madeleine Jotz. We mention some related research projects currently in progress with Ryszard Nest.

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