Differential Topology
 

This course will focus on elements of noncommutative geometry. One of the

aims of noncommutative  geometry is to recast or reobtain theorems in differential

geometry and topology in the language of C* algebras. The course will begin

with two motivating examples, the Gelfand-Naimark theorem on

representations of commutative C* algebras, and the Serre-Swan  theorem on the

equivalence between projective finitely generated C(X) modules, X

a manifold, and vector bundles on the manifold. We will cover some

aspects of K-theory, and end with a discussion of noncommutative cohomologies.
 

Prerequisites: A solid background in differentiable manifolds is required,

and some acquaintance with algebraic topology is desirable.
 

Textbook:

Elements of Noncommutative Geometry,

by J Garcia-Bondia, J. Varilly, and H. Figueroa

Bikhauser Advanced Texts