#### Volume 13, issue 2 (2013)

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Model categories for orthogonal calculus

### David Barnes and Peter Oman

Algebraic & Geometric Topology 13 (2013) 959–999
##### 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 $O\left(n\right)$–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 $O\left(n\right)$–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.

##### Keywords
orthogonal calculus, model categories, spectra, orthogonal spectra
##### Mathematical Subject Classification 2010
Primary: 55P42, 55P91, 55U35
##### Publication
Revised: 10 August 2012
Accepted: 19 September 2012
Published: 5 April 2013
##### Authors
 David Barnes Pure Mathematics Research Centre David Bates Building Queen’s University Belfast BT7 1NN UK http://www.qub.ac.uk/puremaths/Staff/David%20Barnes/index.html Peter Oman Department of Mathematics Southeast Missouri State University One University Plaza Cape Girardeau, MO 63701 USA