On the cohomology of tube structures on compact manifolds

19.12.2022 11:00 - 12:00

Max-Reinhold Jahnke, Marburg

In this talk, I will discuss the cohomology of the differential complex associated with tube-type involutive structures. The main property of the tube-type structures is that they are invariant under the action of a torus, which allows us to use partial Fourier transform with respect to the action of the torus. Fourier series naturally slices the differential complex up into an infinite sequence of elliptical differential complexes, one for each frequency. Therefore, we can apply techniques from sheaf theory and regularity theory for elliptic equations on each slice to obtain information about the original differential complex. With this approach, we developed new techniques that allowed us not only to generalize and better explain results from Hounie-Zugliani, Dattori da Silva-Meziani, Bergamasco-Cordaro-Malagutti, and Bergamasco-Cordaro-Petronilho, but also to prove new results about the finiteness of the cohomology spaces and provide necessary and sufficient conditions for the differential operator at the first degree to have closed range.

Bernhard Lamel

BZ 9, 9. OG, OMP1