English

Calculus III: Taylor Series

Algebraic Topology 2014-11-11 v1

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

Cite

@article{arxiv.math/0310481,
  title  = {Calculus III: Taylor Series},
  author = {Thomas G. Goodwillie},
  journal= {arXiv preprint arXiv:math/0310481},
  year   = {2014}
}

Comments

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper19.abs.html