Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics

# Project C1

## Gauge theoretical methods in manifold theory

Principal Investigator(s) Other Investigators

## Summary:

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.

## Recent Preprints:

 13028 Dirac operators in gauge theory PDF | PS.GZ 12140 Intersection forms of spin four-manifolds PDF | PS.GZ 12136 The moduli space of even surfaces of general type with $K^2=8$, $p_g=4$ and $q=0$ PDF | PS.GZ 12135 Automorphisms of surfaces of general type with $q\leq2$ acting trivially in cohomology PDF | PS.GZ 12130 Pluricanonical maps of stable log surfaces PDF | PS.GZ 12117 A note on the double quaternionic transfer and its $f$-invariant PDF | PS.GZ 12067 Two-dimensional semi-log-canonical hypersurfaces PDF | PS.GZ 12001 Lagrangian fibrations on hyperkähler fourfolds PDF | PS.GZ 11126 Spectral properties of $\operatorname{Spin}^{\mathbb{C}}$ Dirac operators on $T^3$, $S^1 \times S^2$ and $S^3$ PDF | PS.GZ 11125 Fukaya-Seidel category and gauge theory PDF | PS.GZ