Vector bundles and topological K-theory

Lecture Notes

Papers and Books

  • Characteristic classes
    Milnor and Stasheff, 1974.

Additional Resources by Topic

Topological K-theory and Hopf invariant 1 problem

  • 18 Lectures on K-theory
    Ioannis P. Zois, 2010.
    Lecture notes from an Introduction to K-theory course covering topological K-theory, analytic K-theory and higher algebraic K-theory.

Atiyah-Singer index theorem

  • The Index of Elliptic Operators: II
    Michael Atiyah,
    Graeme Segal, 1968.
    This reformulates the result as a sort of Lefschetz fixed point theorem, using equivariant K-theory. This makes it more challenging on first approach.