Arone, Gregory; Ching, Michael Goodwillie calculus. (English) Zbl 1476.55031 Miller, Haynes (ed.), Handbook of homotopy theory. Boca Raton, FL: CRC Press. CRC Press/Chapman Hall Handb. Math. Ser., 1-38 (2020). The Handbook of homotopy theory has been reviewed in [Zbl 1468.55001].Summary: Goodwillie calculus is a method for analyzing functors that arise in topology. One may think of this theory as a categorification of the classical differential calculus of Newton and Leibnitz, and it was introduced by Tom Goodwillie in a series of foundational papers. The nature of Goodwillie calculus lends itself to both computational and conceptual applications. Goodwillie originally developed the subject in order to understand more systematically certain calculations in algebraic \(K\)-theory, and this area remains a compelling source of specific examples. The chapter focuses on Goodwillie’s calculus of homotopy functors, there are two other theories of “calculus” developed by Michael Weiss that are inspired by, and related to, Goodwillie calculus to varying degrees. They are called manifold calculus and orthogonal calculus. The basic concepts of Goodwillie calculus are very general and can be applied to a wide variety of homotopy-theoretic settings.For the entire collection see [Zbl 1468.55001]. Cited in 1 ReviewCited in 1 Document MSC: 55P65 Homotopy functors in algebraic topology 18F50 Goodwillie calculus and functor calculus 55-02 Research exposition (monographs, survey articles) pertaining to algebraic topology Keywords:polynomial approximation; Taylor tower; homogeneous functors; operads; Tate data; algebraic \(K\)-Theory; infinity-categories; manifold calculus; orthogonal calculus Citations:Zbl 1468.55001 PDFBibTeX XMLCite \textit{G. Arone} and \textit{M. Ching}, in: Handbook of homotopy theory. Boca Raton, FL: CRC Press. 1--38 (2020; Zbl 1476.55031) Full Text: DOI arXiv