#### Volume 7, issue 2 (2003)

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 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
Calculus III: Taylor Series

### Thomas G Goodwillie

Geometry & Topology 7 (2003) 645–711
 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 $\left(n-1\right)$–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
Secondary: 55U99