Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 8, Number 4 (2008), 2109-2129.
Topological nonrealization results via the Goodwillie tower approach to iterated loopspace homology
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 obtained from the Goodwillie tower for . Much of the paper develops basic properties of this spectral sequence.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 55S10: Steenrod algebra
Secondary: 55T20: Eilenberg-Moore spectral sequences [See also 57T35] 55S12: Dyer-Lashof operations
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. https://projecteuclid.org/euclid.agt/1513796927