Comparing the orthogonal and homotopy functor calculi

David Barnes, Rosona Eldred

Research output: Contribution to journalArticle

203 Downloads (Pure)

Abstract

Goodwillie’s homotopy functor calculus constructs a Taylor tower of approximations toF , often a functor from spaces to spaces. Weiss’s orthogonal calculus provides a Taylortower for functors from vector spaces to spaces. In particular, there is a Weiss towerassociated to the functor V ÞÑ FpSVq, where SVis the one-point compactification of V .In this paper, we give a comparison of these two towers and show that when F isanalytic the towers agree up to weak equivalence. We include two main applications, oneof which gives as a corollary the convergence of the Weiss Taylor tower of BO. We alsolift the homotopy level tower comparison to a commutative diagram of Quillen functors,relating model categories for Goodwillie calculus and model categories for the orthogonal calculus.
Original languageEnglish
Pages (from-to)3650–3675
Number of pages26
JournalJournal of Pure and Applied Algebra
Volume220
Issue number11
Early online date24 May 2016
DOIs
Publication statusPublished - Nov 2016

Fingerprint Dive into the research topics of 'Comparing the orthogonal and homotopy functor calculi'. Together they form a unique fingerprint.

  • Cite this