## MAT1341F Topics in Differential Geometry: Index Theory

**Classes:** MWF10 in BA6183

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.**