University of Pennsylvania

DRL 4N30

The first two lectures will present an overview of vector bundles and Stiefel-Whitney classes, corresponding to the content of Math 618 this past fall. After that, we will follow the book "Characteristic Classes" by Milnor and Stasheff, beginning with Chapter 9. Oriented Bundles and the Euler Class. Our goal will be to finish most of the book, and do some applications as well, in particular to present Milnor's proof of the existence of exotic differentiable structures on spheres, which uses Pontryagin classes. After the first two meetings, the format of the seminar will be to have lectures by the participants. The various chapters in Milnor-Stasheff typically end with about five interesting problems, some of them quite challenging, and solutions to these can also be presented at the seminar meetings. Please let us know by e-mail to <gluck@math.upenn.edu> and <mmerling@math.upenn.edu> if you are planning to come to the first meeting of the seminar on Tuesday January 22: we will order pizza for that meeting, and it will reduce guesswork to have a reasonably accurate count of who is coming.