The Goodwillie tower of the identity functor and the unstable periodic homotopy of spheres
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We investigate Goodwillie's “Taylor tower” of the identity functor from spaces to spaces. More specifically, we reformulate Johnson's description of the Goodwillie derivatives of the identity, and prove that in the case of an odd-dimensional sphere the only layers in the tower that are not contractible are those indexed by powers of a prime. Moreover, in the case of a sphere the tower is finite in v k -periodic homotopy.
- The Goodwillie tower of the identity functor and the unstable periodic homotopy of spheres
Volume 135, Issue 3 , pp 743-788
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- A1. Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, IL 60637, USA (E-mail address: firstname.lastname@example.org), US
- A2. Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60288-2730, USA, US