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arXiv · 0806.3281

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

Nicholas J. Kuhn
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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.

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BibTeXRIS

Nicholas J. Kuhn. 2008-06-19. Topological nonrealization results via the Goodwillie tower approach to iterated loopspace homology. https://doi.org/10.2140/agt.2008.8.2109

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