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

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

2008-06-19

arxiv.org/abs/0806.3281v1

Mathematics

Algebraic Topology

18 pages

Scientific paper

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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