K-theory Loop Groups and moduli of principal bundles on Riemann surfaces
The lecture notes are preliminary and may contain mistakes. If you find any, feel welcome to email me.
- Plan of the course. Topological K-theory. The Index theorem.
Older notes: Moduli of bundles,
- Twisted K-theory using Fredholm operators
- Gerbes. Mayer-Vietoris calculations.
- Chern character and its twisted versions
- K_G(G). Weyl character formula. Graded twistings
- Moduli of G-bundles
on a Riemann surface and the universal index formula (KITP, 2003)
The full and chiral WZW models (MSRI, 2014)
- Group laws and cohomology theories (Mistakes fixed, almost ready)
- Twisted K-theory and equivariant elliptic cohomology
- Hatcher: Vector bundles and K-theory.
- Atiyah: K-theory
- Segal: Equivariant K-theory (IHES Publications 34, 1968)
- Atiyah, Segal: Equivariant K-theory and Completion, J. Diff Geometry
- Freed, Hopkins: Teleman, Loop Groups and K-theory I, J. Topology 4 (2011)
- Donovan, Karoubi: IHES Publications 38, 1970 (torsion twistings)
- Bouwknegt, Carey et al: Twisted K-theory and K-theory of bundle gerbes, CMP 228 (2002)
- Atiyah, Segal: Twisted K-theory 1, 2; Ukr. Math. Bull 1, 2004
- Freed, Hopkins, Teleman: Twisted equivariant K-theory with complex coefficients, J. Topology 1, 2008
- Freed's ICM lecture
- Lurie, A survey of elliptic cohomology