Geodesic
The Goodwillie tower for S1 and Kuhn’s Theorem
Behrens, Mark1
1Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge MA 02139, USA
Algebraic and Geometric Topology, Tome 11 (2011) no. 4, pp. 2453-2475
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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.

DOI : 10.2140/agt.2011.11.2453
Classification : 55P65, 55Q40, 55S12
Keywords: Whitehead Conjecture, Goodwillie calculus, Dyer–Lashof operation

Behrens, Mark  1

1 Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge MA 02139, USA 
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Behrens, Mark. The Goodwillie tower for S1 and Kuhn’s Theorem. Algebraic and Geometric Topology, Tome 11 (2011) no. 4, pp. 2453-2475. doi: 10.2140/agt.2011.11.2453

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