MATH 7520: Berstein Seminar in Topology (Spring 2012)

Instructor: Tara Holm

The goal of this course is to investigate topics in equivariant topology. We will begin with 2–3 weeks of lectures by the instructor, followed by lectures by the participants. As such, the exact topics will depend on the participants’ specific interests. I propose as a starting point the book, Equivariant homotopy and cohomology theory by Peter May. There should be plenty of topics in this compendium to keep us going for the semester, but we can be flexible if our interests move in a particular direction. I plan to start with cohomology theories, the Borel and Bredon versions of equivariant cohomology, and Smith theory. From there, natural further topics include equivariant K-theory, equivariant stable homotopy, and equivariant cobordism. Of course, I would prefer to have enough students so as to make the seminar not overly onerous. So if you have slightly different interests and aims, please come discuss them with me!

Prerequisites: I will assume that participants have had a first course in algebraic topology (at least Chapters 2 and 3 of Hatcher’s Algebraic Topology, and hopefully Chapter 1 as well). Depending on your backgrounds, we may need to work through parts of Chapter 4 of Hatcher before discussing the more advanced topics in May’s book.