Model categories for orthogonal calculus

David Barnes, Peter Oman

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

We restate the notion of orthogonal calculus in terms of model categories. This provides a cleaner set of results and makes the role of O(n)-equivariance clearer. Thus we develop model structures for the category of n-polynomial and n-homogeneous functors, along with Quillen pairs relating them. We then classify n-homogeneous functors, via a zig-zag of Quillen equivalences, in terms of spectra with an O(n)-action. This improves upon the classification theorem of Weiss. As an application, we develop a variant of orthogonal calculus by replacing topological spaces with orthogonal spectra.
Original languageEnglish
Pages (from-to)959-999
Number of pages41
JournalAlgebraic and Geometric Topology
Volume13
Issue number2
DOIs
Publication statusPublished - 05 Apr 2013

ASJC Scopus subject areas

  • Geometry and Topology

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