Math 460 Algebraic Topology II

Paul Goerss

Class Overview

This quarter we will study unstable modules and algebras over the Steenrod algebra. The main goal of the course will be to prove Sullivan's fixed point conjecture for the action of an elementary p-group on a finite CW complex, but this is case where the journey is at least as interesting as the destination. Along the way we will study the homological algebra of unstable modules, Brown-Gitler spectra, and Lannes's T-functor. One of the charms of this material is that we can begin at a relatively basic level and the class should be accessible to anyone with a decent background in algebraic topology and a certain amount of sophistication. There is also a basic reference:

Lionel Schwartz, Unstable modules over the Steenrod Algebra and Sullivan's fixed point conjecture University of Chicago 1994.