Volume 8, issue 4 (2008)

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

Nicholas Kuhn

Algebraic & Geometric Topology 8 (2008) 2109–2129
Abstract

We prove a strengthened version of a theorem of Lionel Schwartz [Invent. Math. 134 (1998) 211–227] 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 ${H}^{\ast }\left({\Omega }^{n}X;ℤ∕2\right)$ obtained from the Goodwillie tower for ${\Sigma }^{\infty }{\Omega }^{n}X$. Much of the paper develops basic properties of this spectral sequence.

Keywords
loopspace homology, Goodwillie towers
Mathematical Subject Classification 2000
Primary: 55S10
Secondary: 55T20, 55S12
Publication
Received: 8 July 2008
Revised: 10 October 2008
Accepted: 13 October 2008
Published: 19 November 2008
Authors
 Nicholas Kuhn Department of Mathematics University of Virginia Charlottesville, VA 22904 USA