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The Goodwillie tower
for $S^1$ and Kuhn's Theorem
Mark Behrens |
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Algebraic & Geometric Topology 11 (2011) 2453–2475
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Abstract |
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We analyze the homological behavior of the attaching maps in the –local Goodwillie tower of the identity evaluated at . We show that they exhibit the same homological behavior as the James–Hopf maps used by N Kuhn to prove the –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 at the prime . |
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Keywords
Whitehead Conjecture, Goodwillie calculus, Dyer–Lashof
operation
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Mathematical Subject Classification 2010
Primary: 55P65
Secondary: 55Q40, 55S12
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References |
Publication
Received: 29 December 2010
Revised: 1 August 2011
Accepted: 4 August 2011
Published: 6 September 2011
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Authors |
| Mark Behrens | |
| Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Ave Cambridge MA 02139 USA |
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| http://math.mit.edu/~mbehrens | |
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