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

Author: Nicholas J. Kuhn

Email: njk4x at virginia.edu

Address: University of Virginia, Charlottesville, VA 22904

AMS classification number: 55S10

arXiv:0806.3281

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.