Title: Deconstructing Hopf spaces
Authors: Natalia Castellana, Juan A. Crespo, Jerome Scherer
email: natalia@mat.uab.es, JuanAlfonso.Crespo@uab.es,
jscherer@mat.uab.es
AMS classification number: 55P45; 55S10; 55P60; 55P47; 55S45
Abstract: We characterize Hopf spaces with finitely generated
cohomology as algebra over the Steenrod algebra. We ``deconstruct"
the original space into an H-space Y with finite mod p cohomology
and a finite number of p-torsion Eilenberg-Mac Lane spaces. One
reconstructs X from Y by taking extensions by principal
H-fibrations. We give a precise description of homotopy
commutative H-spaces in this setting and give a criterion to
recognize connected covers of H-spaces with finite mod p
cohomology. The key observation is that the module of
indecomposables lies in some stage of the Krull filtration of the
category of unstable modules over the Steenrod algebra. We compare
this algebraic condition with a topological one, namely that some
iterated loop space of X is BZ/p-local.