Natalia Castellana - "Loop spaces with noetherian mod p cohomology"
(with J.A. Crespo and J. Scherer)
In this project we study topological spaces whose loop space has
Noetherian mod p cohomology. The aim is to describe the difference
between loop spaces with finite mod p cohomology and those
whose mod p cohomology is a finitely generated algebra. In the first
case, p-complete mod p finite loop spaces lead to the notion of a
p-compact group introduced by Dwyer and Wilkerson who showed that then
the mod p cohomology of their classifying space is Noetherian.
Moreover, p-compacts have been recently classified. We also prove that
the classifying space of a loop space with noetherian mod p cohomology
has finitely generated mod p cohomology as an algebra over the Steenrod
algebra with the following restriction: the module of indecomposable
elements belong to the second stage of the Krull filtration U_1 of the
category U of unstable modules over the Steenrod algebra.