Volume 11, issue 4 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The Goodwillie tower for $S^1$ and Kuhn's Theorem

Mark Behrens

Algebraic & Geometric Topology 11 (2011) 2453–2475
Abstract

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.

Keywords
Whitehead Conjecture, Goodwillie calculus, Dyer–Lashof operation
Mathematical Subject Classification 2010
Primary: 55P65
Secondary: 55Q40, 55S12
References
Publication
Received: 29 December 2010
Revised: 1 August 2011
Accepted: 4 August 2011
Published: 6 September 2011
Authors
Mark Behrens
Department of Mathematics
Massachusetts Institute of Technology
77 Massachusetts Ave
Cambridge MA 02139
USA
http://math.mit.edu/~mbehrens