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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
##### Keywords:
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