Principal bundles, spin geometry and Index Theory

Seiberg-Witten Theory

Morse Theory and Floer Theory

Stable homotopy theory and equivariant cohomology

Stable homotopy invariants for the 4-dimensional Seiberg-Witten equations

Conley Index Theory

Stable homotopy types for Seiberg-Witten Floer homology

Triangulation conjecture and Hauptvermutung

And check out the many links on the following website:

Other stable homotopy types in low-dimensional topology