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 language | English |
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Pages (from-to) | 959-999 |
Number of pages | 41 |
Journal | Algebraic and Geometric Topology |
Volume | 13 |
Issue number | 2 |
DOIs | |
Publication status | Published - 05 Apr 2013 |
ASJC Scopus subject areas
- Geometry and Topology