The cohomology of left-invariant involutive structures

• Applicant: Dr. Max Jahnke
• Subject Area: Mathematics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 511126884

It is well known that the De Rham cohomology of a compact Lie group is isomorphic to the Chevalley-Eilenberg cohomology. While the former is a topological invariant of the Lie group, the latter can be computed by using simple linear algebra methods. Our goal is to understand if it is possible to obtain a similar isomorphism between the cohomology spaces associated with invariant involutive structures and the cohomology of a generalized Chevalley-Eilenberg complex. By combining the applicant's expertise in Partial Differential Equations and Analysis with Prof. Dr. Rollenske's expertise in Complex Geometry, we believe that it is possible to obtain new exciting results in the cases of elliptic and CR involutive structures defined over a compact Lie group or a compact nilmanifold. The results will provide new insights in the general theory of involutive structures as, for example, they reveal algebraic obstructions for solvability for the associated differential complexes.

• DFG Programme: WBP Position