ABSTRACT

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.