Math 690 (Phillips)

This is the home page for N. C. Phillips' Math 690 at the University of Oregon, Fall quarter 2016. Right now, only administrative information is posted here. Any additional material will be posted here, not on Canvas. (I do not use Canvas.)

Update 26 September: Starting Wednesday 28 September, we will meet in 209 Deady (not 206 Deady). Also, the enrollment limit is now supposed to be 27.

A general comment: This course is about topological K-theory, not the K-theory of C*-algebras.

To the topologists: I will make only occasional comments about the relation to C*-algebras, which can safely be ignored if you don't know about or are not interested in C*-algebras.

To the functional analysts: I will make occasional comments about the relation to K-theory of Banach algebras. Since they will be brief, they will not be meaningful unless you have already seen K-theory of C*-algebras or Banach algebras. However, some of the methods (in particular involving homotopy of mapping cones and mapping cylinders), while not normally presented in a first introduction to K-theory of C*-algebras, are easily adaptable to the C*-algebra setting and play a very important role there. In any case, anyone making serious use of K-theory of C*-algebras should understand its connection with topology.

Course information:

Course outline:

  1. Operations on vector bundles over compact spaces.
  2. Definition of K-theory and first properties.
  3. Bott periodicity.
  4. K-theory as a cohomology theory.
  5. Products in K-theory.
  6. The Thom isomorphism and computations of K-theory in other examples.
  7. If time: application to the Hopf invariant problem.

Homework problems: pdf; AMSLaTeX. Last updated: 25 September 2016. Warning: Almost no proofreading has been done!

Possible topics for a course on equivariant K-theory: pdf; AMSLaTeX. (This was put together at the request of a student several years ago. The course was never offered, and I am not aware of there being enough interest to offer it in the future. Just take the list of topics as telling you about one further direction in K-theory which exists.) Warning: No proofreading has been done!

This page maintained by N. Christopher Phillips, email.

Last significant change 25 September 2016.