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Topological K-Theory

2019 – 2020, IX семестр

Информация по курсу

Section 1: K-groups
1. The K-group of complex vector bundles.
2. The Bott periodicity theorem.
3. Difference constructions.
4. The cohomology theory.
5. Examples of computation of K-groups.
6. Non-parallelizability of real projective spaces.
7. The Thom isomorphism.

Section 2: The Chern character and its applications
1. The Chern character
2. Computation of rational K-groups.
3. Integrality theorems.
4. Non-embeddability theorems.

Section 3: The Adams operations and their applications
1. The Adams operations.
2. Evenness of the Hopf invariant.
3. Non-parallelizability of spheres.
4. The Adams invariant.
5. The real K-theory.