Fibre bundles

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Preliminaries on homotopy theory

pt. I. The general theory of fibre bundles. Generalities on bundles

Vector bundles

General fibre bundles

Local coordinate description of fibre bundles

Change of structure group in fibre bundles

Calculations involving the classical groups

pt. II. Elements of K-theory. Stability properties of vector bundles

Relative K-theory

Bott periodicity in the complex case

Clifford Algebras

The Adams operations and representations

Representation rings of classical groups

The Hopf invariant

Vector fields on the sphere

pt. III. Characteristic classes. Chern classes and Stiefel-Whitney classes

Differentiable manifolds

General theory of characteristic classes

Appendix: Dold's theory of local properties of bundles