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
Type of course
Mode
Requirements
Prerequisites
Prerequisites (description)
Course coordinators
Learning outcomes
Students understands equivariant cohomology theories and their applications
Assessment criteria
Oral exam proceeded by a written test. 30% of the evaluation based on activity during problem sessions
Bibliography
Neil Chriss, Victor Ginzburg, Representation Theory and Complex Geometry
https://link.springer.com/book/10.1007/978-0-8176-4938-8).
Friedrich Hirzebruch, Thomas Berger , Rainer Jung
Manifolds and Modular Forms https://link.springer.com/book/10.1007/978-3-663-10726-2
D. Husemöller , M. Joachim , B. Jurčo , M. Schottenloher,
Basic Bundle Theory and K-Cohomology Invariants
https://link.springer.com/book/10.1007/978-3-540-74956-1
Oryginalne prace badawcze: Atiyah, Segal, Matumoto, Landweber, Ganter, Okounkov i inne
Additional information
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