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.

**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