Topics in algebraic topology: the sullivan conjecture

Lectures: 3 sessions / week, 1 hour / session

Let G be a finite p-group acting on a nice topological space X. The Sullivan conjecture asserts that the p-adic homotopy type of the fixed point set can be recovered from the action of G on the p-adic completion of the homotopy type of X. The goal of this course is to describe some of the tools (the theory of unstable modules over the Steenrod algebra) which enter into the proof of Sullivan's conjecture.

Algebraic Topology II, (18.906). A working knowledge of modern algebraic topology will be assumed, but all of the calculational machinery (such as the Steenrod algebra) will be constructed from scratch.

We will loosely follow the book:

Schwartz, Lionel. Unstable Modules over the Steenrod Algebra and Sullivan's Fixed Point Set Conjecture. Chicago, IL: University of Chicago Press, 1994. ISBN: 9780226742021.

Course grade is based upon class attendance and participation. There are no homework assignments, projects, or exams.

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