MAT1352F Index Theory

Classes: T 12-1 BA 6183, F 9:30-11 RS 310 (please note the new time!)

Course description

This course will be an introduction to the Atiyah-Singer index theorem for elliptic operators. We will cover the following topics:

  • The index of Fredholm operators
  • Elliptic differential operators
  • K-theory
  • The Atiyah-Singer index theorem
  • Cohomological formulas
  • Applications

    Prerequisites: Solid background knowledge in algebraic topology and manifold theory, as well as some Hilbert space basics.

    If you are taking this course for credit, click here .

    References

  • Michael Atiyah, Iz Singer: The index of elliptic operators I.

  • Nigel Higson, John Roe: Lectures on Operator K-theory and the Atiyah-Singer Index Theorem.

  • Thierry Fack: Index theorems and non-commutative topology.

  • Nigel Higson: On the K-theory proof of the index theorem.

  • Bernhelm Booss-Bavnbeck, David Bleecker: Topology and analysis. The first few chapters of a revised version are posted here.

  • Blaine Lawson, Louise Michelson: Spin geometry.

  • Dan Freed: Lecture Notes.

  • Liviu Nicolaescu: Lecture Notes.