Gauge theoretical methods in manifold theory
Gauge theoretic methods have proved to be quite effective in investigating smooth manifolds, most prominent in dimensions 3 and 4. According to physical arguments, the manifold invariants derived from these methods should fit into some general picture of topological quantum field theories (TQFT). Supporting evidence abound and partial constructions realising essential features of a TQFT have been constructed. Despite many mathematical discoveries, the picture is far from being complete. The project aims at a structural understanding of gauge theoretic invariants and their relationships. In particular, it is intended to explore the reach of the stable cohomotopy approach (Bauer and Furuta 2004, Bauer 2004, Bauer 2005) and to extend it to a topological quantum field theory.
This project continues the successful work of the project Gauge theoretical invariants of three-and four-dimensional manifolds under the direction of Kim Frøyshov and Stefan Bauer.