Localization, Periodicity, and Galois Symmetry (Spring 2023)

Sullivan introduced the idea of localizing and completing spaces at primes, which led to important advances in topology and homotopy theory. For example, it allowed natural actions of the Galois groups on objects associated to manifolds to be studied in relation with periodicity theorems. One concrete result of this theory is the proof of the Adams conjecture using etale homotopy. We will follow Sullivan's notes [S2] in this seminar. Aside from some algebraic topology which we will spend some time reviewing, these notes build this theory essentially from scratch.

Schedule

Jan 30
Caleb Ji
Organizational meeting, Algebraic constructions
We will explain the plan for this seminar and begin Chapter 1 of [S1]. We will spend some extra time reviewing sme topological background, including equivariant cohomology and K-theory.