Geodesic
Topological nonrealization results via the Goodwillie tower approach to iterated loopspace homology
Kuhn, Nicholas1
1Department of Mathematics, University of Virginia, Charlottesville, VA 22904, USA
Algebraic and Geometric Topology, Tome 8 (2008) no. 4, pp. 2109-2129
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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; ℤ∕2) obtained from the Goodwillie tower for Σ∞ΩnX. Much of the paper develops basic properties of this spectral sequence.

DOI : 10.2140/agt.2008.8.2109
Keywords: loopspace homology, Goodwillie towers

Kuhn, Nicholas  1

1 Department of Mathematics, University of Virginia, Charlottesville, VA 22904, USA 
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Kuhn, Nicholas. Topological nonrealization results via the Goodwillie tower approach to iterated loopspace homology. Algebraic and Geometric Topology, Tome 8 (2008) no. 4, pp. 2109-2129. doi: 10.2140/agt.2008.8.2109

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