The Goodwillie tower for S^1 and Kuhn's theorem

Details The Goodwillie tower for S^1 and Kuhn's theorem The Goodwillie tower for S^1 and Kuhn's theorem

2010-12-03

arxiv.org/abs/1012.0810v2

Mathematics

Algebraic Topology

v2: 23 pages, clarified exposition in many parts, to appear in AGT

Scientific paper

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^1 at the prime 2.

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