nLab
The Relation of Cobordism to K-Theories

Contents

Context

Algebraic topology

Cobordism theory

This page compiles material related to the book

on cobordism theory and topological K-theory, meeting in the notion of the e-invariant.

Contents

The Thom Isomorphism in K-theory

1. Exterior algebra

2. Tensor products of exterior algebras

3. Application to bundles

4. Thom classes of line bundles

5. Cobordism and homomorphism into K-theory

6. The homomorphism μ c\mu_c

Cobordism Characteristic Classes

7. A theorem of Dold

8. Characteristic classes on cobordism

9. Characteristic classes in K-theory

10. A cobordism interpretation for K *(X)K^\ast(X)

11. Mappings into spheres

UU-Manifolds with Framed Boundaries

12. The UU-bordism groups Ω U\Omega^U_\bullet

13. Characteristic numbers from K-theory

14. The theorem of Stong and Hattori

15. UU-Manifolds with stably framed boundaries

16. The bordism groups Ω U,fr\Omega^{U,fr}_\bullet

17. The groups Ω U,SU\Omega^{\mathrm{U}, SU}_\bullet

18. The image of Ω fr\Omega^{fr}_{\bullet} in Ω SU\Omega^{SU}_\bullet

category: reference

Last revised on February 21, 2021 at 06:14:26. See the history of this page for a list of all contributions to it.