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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060

Calculus III: Taylor Series

Thomas G Goodwillie

Geometry & Topology 7 (2003) 645–711

DOI: 10.2140/gt.2003.7.645

arXiv: math.AT/0310481

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 (n-1)–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.

Keywords

Homotopy functor, excision, Taylor tower

Mathematical Subject Classification

Secondary: 55U99

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Publication

Received: 8 November 2002
Accepted: 20 October 2003
Published: 28 October 2003
Proposed: Haynes Miller
Seconded: Ralph Cohen, Gunnar Carlsson

Authors
Thomas G Goodwillie
Department of Mathematics
Brown University
Box 1917
Providence
Rhode Island 02912–0001
USA