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2003 Calculus III: Taylor Series
Thomas G Goodwillie
Geom. Topol. 7(2): 645-711 (2003). DOI: 10.2140/gt.2003.7.645

Abstract

We study functors from spaces to spaces or spectra that preserve weak homotopy equivalences. For each such functor we construct a universal n–excisive approximation, which may be thought of as its n–excisive part. Homogeneous functors, meaning n–excisive functors with trivial (n1)–excisive part, can be classified: they correspond to symmetric functors of n variables that are reduced and 1–excisive in each variable. We discuss some important examples, including the identity functor and Waldhausen’s algebraic K–theory.

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Thomas G Goodwillie. "Calculus III: Taylor Series." Geom. Topol. 7 (2) 645 - 711, 2003. https://doi.org/10.2140/gt.2003.7.645

Information

Received: 8 November 2002; Accepted: 20 October 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1067.55006
MathSciNet: MR2026544
Digital Object Identifier: 10.2140/gt.2003.7.645

Subjects:
Secondary: 55U99

Rights: Copyright © 2003 Mathematical Sciences Publishers

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