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The Goodwillie tower for \(S^1\) and Kuhn’s theorem. (English) Zbl 1230.55007
Consider the spectral sequence for the integral Eilenberg-MacLane spectrum obtained from its filtration by the symmetric powers of the sphere spectrum. Kuhn’s theorem, also known as the Whitehead conjecture, says that \(2\)-locally this spectral sequence collapses at the \(E_2\) page. In this paper, the author proves an analogous result for the \(2\)-local Goodwillie tower of the identity at the \(1\)-sphere \(S^1\): it collapses at the \(E_2\) page, and the Whitehead sequence yields a contracting homotopy.

MSC:
55P65 Homotopy functors in algebraic topology
55Q40 Homotopy groups of spheres
55S12 Dyer-Lashof operations
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