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Goodwillie towers and chromatic homotopy: an overview. (English) Zbl 1105.55002

Ando, Matthew (ed.) et al., Proceedings of the Nishida Fest conferences on homotopy theory, Kinosaki, Japan, July 28–August 1 2003 and August 4–8, 2003. Dedicated to Gôrô Nishida on the occasion of his 60th birthday. Coventry: Geometry & Topology Publications. Geometry and Topology Monographs 10, 245-279 (2007).
Summary: 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.
For the entire collection see [Zbl 1104.00015].

MSC:

55N20 Generalized (extraordinary) homology and cohomology theories in algebraic topology
55P43 Spectra with additional structure (\(E_\infty\), \(A_\infty\), ring spectra, etc.)
55P47 Infinite loop spaces
18G55 Nonabelian homotopical algebra (MSC2010)
55-02 Research exposition (monographs, survey articles) pertaining to algebraic topology
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