Seiberg-Witten and stable homotopy theory
Topics
Potential talk topics
- Principal bundles and classifying spaces
- Spin, spin^c, Clifford multiplication
- Spinor bundles and Dirac operators
- Fredholm operators and the Atiyah-Singer Index Theorem
- SW equations, monopole map and Coulomb gauge slice
- Equivariant Seiberg-Witten Floer theory
- Vector fields on manifolds and index
- Morse theory and the Cohen-Jones-Segal construction
- Conley Index Theory
- Equivariant cohomology
- Stable homotopy theory 1 - basic
- Stable homotopy theory 2 - invariants and Spanier-Whitehead duality
- The Seiberg-Witten Floer stable homotopy type
- The triangulation conjecture 1 - manifold structures, Kirby-Siebenmann and Rochlin invariants
- The triangulation conjecture 2 - history of the triangulation problem and the Hauptvermutung
- The triangulation conjecture 3 - solution by Casson and Manolescu