Calculus III: Taylor Series

Goodwillie, Thomas G¹

¹ Department of Mathematics, Brown University, Box 1917, Providence, Rhode Island 02912–0001, USA

Geometry & topology, Tome 7 (2003) no. 2, pp. 645-711.

Résumé

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.

Détail

DOI : 10.2140/gt.2003.7.645

Keywords: Homotopy functor, excision, Taylor tower

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