MAT1341F Topics in Differential Geometry: Index Theory

Classes: MWF10 in BA6183

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.


  • 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.

  • Blaine Lawson, Louise Michelson: Spin geometry.

  • Liviu Nicolaescu: Lecture Notes.