The Goodwillie Calculus of Functors

Abstract

The purpose of this meeting was to introduce the participants to calculus of functors, a theory aimed at “approximating” functors in algebra and topology. The focus of the talks was on two related branches of the theory, homotopy and manifold calculus. T

he organizers, Thomas Goodwillie and Randy McCarthy, scheduled 16 talks. The first was given by Goodwillie who introduced the main ideas and outlined the plan for the rest of the meeting. In talks 2–5, speakers explained the most important terminology, techniques, and results used in both versions of the theory. In talks 6–8, participants learned about manifold calculus and how it applies to spaces of knots (talk 8), while talks 9–15 dealt with homotopy calculus. In the last four of those lectures, some applications, elaborations on results established in previous talks, and different versions of certain ideas and proofs encountered so far were given. Goodwillie explored some connections between the two versions of calculus of functors (as they apply to the embedding and identity functors) and gave the concluding remarks in the last talk.

It should be noted that a third version of the theory, orthogonal calculus, was not discussed due to time constraints, but Goodwillie explained some of its most salient features in an extra evening session. Other evening events took place as well, such as Rainer Vogt's elaboration of an aspect of his talk and informal research reports given by some participants.