Index Theory on Submanifold Complements (B09*)

• Subject Area: Mathematics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 224262486

We study boundary conditions for Dirac operators defined on submanifold complements, i.e., on incomplete manifolds obtained by removing a submanifold from a complete Riemannian manifold. In a coarse geometric approach, we will view these boundary conditions as a lift from locally finite K-homology to K-homology. The project has applications to link invariants, obstructions to positive scalar curvature metrics on non-spin manifolds, and topological insulators.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1085: Higher Invariants – Interactions between Arithmetic Geometry and Global Analysis
• Applicant Institution: Universität Regensburg
• Project Heads: Professor Dr. Bernd Eberhard Ammann; Professor Dr. Ulrich Bunke; Dr. Matthias Ludewig