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Transactions of the American Mathematical Society

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Splitting criteria for homotopy functors of spectra


Author: Phichet Chaoha
Journal: Trans. Amer. Math. Soc. 356 (2004), 1271-1280
MSC (2000): Primary 55P65
Published electronically: November 4, 2003
MathSciNet review: 2034308
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Abstract | References | Similar Articles | Additional Information

Abstract: We explore the interaction between the Taylor tower and cotower, as defined in deriving calculus with cotriples and dual calculus for functors to spectra of functors of spectra. This leads to new splitting criteria which generalize the results in dual calculus for functors to spectra.


References [Enhancements On Off] (What's this?)

  • 1. P. Chaoha, Obstructions to constructing the Taylor tower of finite degree functors of spectra, Ph.D. thesis, UIUC, May 2001.
  • 2. Thomas G. Goodwillie, Calculus. I. The first derivative of pseudoisotopy theory, 𝐾-Theory 4 (1990), no. 1, 1–27. MR 1076523, 10.1007/BF00534191
  • 3. Thomas G. Goodwillie, Calculus. II. Analytic functors, 𝐾-Theory 5 (1991/92), no. 4, 295–332. MR 1162445, 10.1007/BF00535644
  • 4. T. Goodwillie, Calculus III: Taylor series of a homotopy functor, in preparation.
  • 5. B. Johnson and R. McCarthy, Deriving calculus with cotriples, Trans. Amer. Math. Soc. 356 (2004), 757-803.
  • 6. Randy McCarthy, Dual calculus for functors to spectra, Homotopy methods in algebraic topology (Boulder, CO, 1999) Contemp. Math., vol. 271, Amer. Math. Soc., Providence, RI, 2001, pp. 183–215. MR 1831354, 10.1090/conm/271/04357

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Additional Information

Phichet Chaoha
Affiliation: Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
Email: phichet.c@chula.ac.th

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03429-9
Keywords: Homotopy functors, calculus of functors
Received by editor(s): August 6, 2001
Published electronically: November 4, 2003
Dedicated: This paper is dedicated to the author’s beloved wife and daughter: Cherry and Cheese
Article copyright: © Copyright 2003 American Mathematical Society