Calculus III: Taylor Series

Details Calculus III: Taylor Series Calculus III: Taylor Series

2003-10-30

arxiv.org/abs/math/0310481v1

Geom. Topol. 7(2003) 645-711

Mathematics

Algebraic Topology

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

Scientific paper

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.

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