Equivariant K-theory and elliptic cohomology 1000-1M25EKE

1. General concept of G-CW complexes and equivariant cohomology theory

2. The localization theorem for torus actions according to tom Dieck, within the framework of general equivariant cohomology theories

3. Equivariant K-theory of vector bundles - topological version according to Segal:

* constructions on vector bundles
* Thom isomorphism (Koszul complex)
* extension of K-theory of bundles to a cohomology theory
* applications of equivariant K-theory in algebraic geometry
* K-theory of flag varieties, Demazure operations, and the Hecke algebra

4. Basic knowledge on the application of modular forms in topology:

* elliptic genus in the non-equivariant case
* elliptic cohomology via the Landweber exact functor theorem

5. Equivariant elliptic cohomology for torus actions:

* application to flag varieties