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2011 The Goodwillie tower for $S^1$ and Kuhn's Theorem
Mark Behrens
Algebr. Geom. Topol. 11(4): 2453-2475 (2011). DOI: 10.2140/agt.2011.11.2453


We analyze the homological behavior of the attaching maps in the 2–local Goodwillie tower of the identity evaluated at S1. We show that they exhibit the same homological behavior as the James–Hopf maps used by N Kuhn to prove the 2–primary Whitehead conjecture. We use this to prove a calculus form of the Whitehead conjecture: the Whitehead sequence is a contracting homotopy for the Goodwillie tower of S1 at the prime 2.


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Mark Behrens. "The Goodwillie tower for $S^1$ and Kuhn's Theorem." Algebr. Geom. Topol. 11 (4) 2453 - 2475, 2011.


Received: 29 December 2010; Revised: 1 August 2011; Accepted: 4 August 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1230.55007
MathSciNet: MR2835236
Digital Object Identifier: 10.2140/agt.2011.11.2453

Primary: 55P65
Secondary: 55Q40 , 55S12

Keywords: Dyer–Lashof operation , Goodwillie calculus , Whitehead Conjecture

Rights: Copyright © 2011 Mathematical Sciences Publishers

Vol.11 • No. 4 • 2011
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