The Goodwillie tower for S[superscript 1] and Kuhn's Theorem

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.