Goodwillie towers and chromatic homotopy: an overview

Abstract

This paper is based on talks I gave in Nagoya and Kinosaki in August of 2003. I survey, from my own perspective, Goodwillie's work on towers associated to continuous functors between topological model categories, and then include a discussion of applications to periodic homotopy as in my work and the work of Arone-Mahowald.

This is the version published by Geometry & Topology Monographs on 29 January 2007

References in corpus (2)

• Homology and Cohomology of E-infinity Ring Spectra
• Tate cohomology and periodic localization of polynomial functors

Cited by in corpus (27)

• Calculus of functors and model categories II
• Gauge enhancement of super M-branes via parametrized stable homotopy theory
• Calculus of functors and model categories
• Homotopical resolutions associated to deformable adjunctions
• Homotopy completion and topological Quillen homology of structured ring spectra
• A general context for Goodwillie Calculus
• Goodwillie's Calculus of Functors and Higher Topos Theory
• Homotopy nilpotent groups
• Introduction to the manifold calculus of Goodwillie-Weiss
• Rational Homotopy Calculus of Functors
• Morava E-homology of Bousfield-Kuhn functors on odd-dimensional spheres
• A Monoidal Model for Multilinearization
• A multiplicative comparison of MacLane homology and topological Hochschild homology
• A chain rule for Goodwillie derivatives of functors from spectra to spectra
• The spectrum of excisive functors
• The Goodwillie tower for S^1 and Kuhn's theorem
• The Segal Conjecture for topological Hochschild homology of the Ravenel spectra
• Combinatorial models for Taylor polynomials of functors
• Parametrised Homotopy Theory and Gauge Enhancement
• On calculus of functors in model categories
• Goodwillie calculus in the category of algebras over a chain complex operad
• Cofibrantly generated model structures for functor calculus
• Derived Character Maps of Groups Representations
• The localization of orthogonal calculus with respect to homology
• Goodwillie tower of the norm functor
• A guide to telescopic functors
• A variant of a Dwyer-Kan theorem for model categories