Secondary invariants for foliations

• Applicants: Dr. Sara Azzali; Professor Dr. Sebastian Goette
• Subject Area: Mathematics
• Term: from 2017 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 339667958

Secondary invariants such as eta, rho and torsion forms are important mathematical objects relating in a deep way spectral aspects to geometric and topological properties of the underlying space. They are involved in geometric refinements of index formulae, as well as classification and rigidity results.The goals of this project are the construction and investigation of their properties on foliated closed manifolds, where the noncompactness of the leaves and the complicated dynamical phenomena make the analysis very challenging. Amongst our objectives are: the computation of the large time limit of the leafwise heat operator's supertrace in the H\ae fliger setting and the investigation of cases where the limit does not agree with the analytic index; a deeper understanding of the noncommutative eta and torsion forms; the further development of the machinery of analytic surgery sequences for foliations; the application of the Igusa-Klein torsion to the distinction of exotic structure on a given foliation.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2026: Geometry at Infinity
• International Connection: France, Italy
• Cooperation Partners: Paolo Antonini, Ph.D.; Professor Dr. Moulay-Tahar Benameur