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

Kuhn, Nicholas

doi:10.2140/agt.2008.8.2109

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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

DOI: 10.2140/agt.2008.8.2109

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 $H^{*} (Ω^{n} X; ℤ ∕ 2)$ obtained from the Goodwillie tower for $Σ^{\infty} Ω^{n} X$ . 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

References

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

Volume 8, issue 4 (2008)