Topology Seminar by Tilman Bauer

Algebra/Topology Seminar

Speaker: Tilman Bauer (KTH Stockholm)

Title: Chromatic unstable homotopy, plethories, and the Dieudonné correspondence

Abstract: Chromatic unstable homotopy theory is the study of the K(n)-local category of spaces, where K(n) is a Morava K-theory. As in the stable setting, we have a fairly good understanding of this category when n=0 or 1, but not for n>1. Of particular interest is the space of maps between two K(n)-local spaces X and Y. There is an unstable Adams (or Bousfield-Kan) spectral sequence based on K(n)-homology to compute the homotopy groups of such mapping spaces, but its E^2-term is a monadic derived functor which is not easily accessible. It can also be described as an Ext term of modules over an algebraic structure called a plethory, which is a kind of Hopf algebroid in the category of coalgebras, which is still quite unwieldy. In this talk, I will explain how Dieudonné theory can be used to understand this structure in much simpler terms, and to do explicit computations.