We analyze the homological behavior of the attaching maps in the 2—local Goodwillie tower of the identity evaluated at S~1 . 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 S' at the prime 2.
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