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
The Atiyah-Singer index theorem
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.
Index theorems and non-commutative topology.
On the K-theory proof of the index theorem.
Bernhelm Booss-Bavnbeck, David Bleecker:
Topology and analysis.
Blaine Lawson, Louise Michelson: