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The Goodwillie Tower Of The Identity Is A Logarithm
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@MISC{Arone_thegoodwillie,
author = {Greg Arone and Marja Kankaanrinta},
title = {The Goodwillie Tower Of The Identity Is A Logarithm},
year = {}
}
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Abstract
. We offer the point of view that the Goodwillie tower of the identity functor is a formal inverse to the standard filtration of stable homotopy in the same sense as ln(x) is inverse to exp(x). 0. Introduction The Goodwillie tower of the identity (see [2, 3, 4] for a general reference on the Goodwillie calculus) is a tower of functors and natural transformations, which starts with stable homotopy and converges to unstable homotopy. The functors in this tower are characterized by certain universal properties, and according to [4] they should be thought of as the Taylor polynomials of the identity. The study of these polynomial approximations was initiated in [5] and continued in [1]. In particular, an explicit description of the fibers in the tower was derived there. However, the nature of the tower and the reason that it converges remained a bit mysterious. It appears that the Goodwillie tower is a natural, canonical object, and therefore one expects to have a basic understanding of i...
Keyphrases
goodwillie tower stable homotopy formal inverse natural transformation certain universal property taylor polynomial identity functor goodwillie calculus explicit description basic understanding unstable homotopy standard filtration general reference canonical object polynomial approximation
