Oberseminar Deformationsquantisierung und Geometrie: Ioan Mărcuț (Universität zu Köln)

Abstract: The main goal of this talk is to introduce closed pseudogroups and their associated sheaf of Lie algebras. For this, the weak C-infinity topology Whitney on the sheaf of smooth sections of a fibre bundle will be discussed. This is used to define closed subsheaves, which generalize the sheaf of solutions to a PDE. The topology on the sheaf of smooth sections has certain particularities, which yields interesting characterizations of closed subsheaves. Finally, the main result of this talk it that closed pseudogroups admit a closed sheaf of Lie algebras, which could be seen as an analog of the Closed-subgroup theorem of Cartan and van Neumann.

This work is part of a larger project, on rigidity of solutions to a PDE with symmetries, and was started in collaboration with Roy Wang. An early version of the results are contained in the PhD thesis of Roy Wang, available here: https://arxiv.org/abs/1712.00808.