Topological nonrealization results via the Goodwillie tower approach to iterated loopspace homology

Abstract

We prove a strengthened version of a theorem of Lionel Schwartz that says that certain modules over the Steenrod algebra cannot be the mod 2 cohomology of a space. What is most interesting is our method, which replaces his iterated use of the Eilenberg--Moore spectral sequence by a single use of the spectral sequence converging to the mod 2 cohomology of Omega^nX obtained from the Goodwillie tower for the suspension spectrum of Omega^nX. Much of the paper develops basic properties of this spectral sequence.

18 pages

References in corpus (1)

• Bocksteins and the nilpotent filtration on the cohomology of spaces

Cited by in corpus (4)

• The mod 2 homology of infinite loopspaces
• The Arone-Goodwillie spectral sequence for ${\Sigma }^{\infty }{\Omega }^n$ and topological realization at odd primes
• Essential extensions, the nilpotent filtration and the Arone-Goodwillie tower
• Correction to ""Topological nonrealization results via the Goodwillie tower approach to iterated loopspace homology"