A chain rule for Goodwillie derivatives of functors from spectra to spectra
Author:
Michael Ching
Journal:
Trans. Amer. Math. Soc. 362 (2010), 399426
MSC (2000):
Primary 55P42, 55P65
Published electronically:
July 2, 2009
MathSciNet review:
2550157
Fulltext PDF Free Access
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Abstract: We prove a chain rule for the Goodwillie calculus of functors from spectra to spectra. We show that the (higher) derivatives of a composite functor at a base object are given by taking the composition product (in the sense of symmetric sequences) of the derivatives of at with the derivatives of at . We also consider the question of finding , and give an explicit formula for this when is homogeneous.
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 Nicholas J. Kuhn, Goodwillie towers and chromatic homotopy: An overview, Proceedings of Nishida Fest (Kinosaki 2003), Geometry and Topology Monographs, vol. 10, 2007, pp. 245279.
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Additional Information
Michael Ching
Affiliation:
Department of Mathematics, University of Georgia, Athens, Georgia 30602
DOI:
http://dx.doi.org/10.1090/S000299470904834X
Received by editor(s):
March 24, 2008
Published electronically:
July 2, 2009
Article copyright:
© Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
