The Goodwillie tower for S1 and Kuhn’s Theorem

Behrens, Mark

doi:10.2140/agt.2011.11.2453

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The Goodwillie tower for $S^1$ and Kuhn's Theorem

Mark Behrens

Algebraic & Geometric Topology 11 (2011) 2453–2475

DOI: 10.2140/agt.2011.11.2453

Abstract

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 $2$ .

Keywords

Whitehead Conjecture, Goodwillie calculus, Dyer–Lashof operation

Mathematical Subject Classification 2010

Primary: 55P65

Secondary: 55Q40, 55S12

References

Publication

Received: 29 December 2010

Revised: 1 August 2011

Accepted: 4 August 2011

Published: 6 September 2011

Authors

Mark Behrens
Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Ave Cambridge MA 02139 USA
http://math.mit.edu/~mbehrens

Volume 11, issue 4 (2011)