Algebraic & Geometric Topology

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

Nicholas Kuhn

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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(ΩnX;2) obtained from the Goodwillie tower for ΣΩnX. Much of the paper develops basic properties of this spectral sequence.

Article information

Algebr. Geom. Topol., Volume 8, Number 4 (2008), 2109-2129.

Received: 8 July 2008
Revised: 10 October 2008
Accepted: 13 October 2008
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55S10: Steenrod algebra
Secondary: 55T20: Eilenberg-Moore spectral sequences [See also 57T35] 55S12: Dyer-Lashof operations

loopspace homology Goodwillie towers


Kuhn, Nicholas. Topological nonrealization results via the Goodwillie tower approach to iterated loopspace homology. Algebr. Geom. Topol. 8 (2008), no. 4, 2109--2129. doi:10.2140/agt.2008.8.2109.

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