Model categories for orthogonal calculus

Barnes, David; Oman, Peter

doi:10.2140/agt.2013.13.959

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Model categories for orthogonal calculus

David Barnes and Peter Oman

Algebraic & Geometric Topology 13 (2013) 959–999

DOI: 10.2140/agt.2013.13.959

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.

Keywords

orthogonal calculus, model categories, spectra, orthogonal spectra

Mathematical Subject Classification 2010

Primary: 55P42, 55P91, 55U35

References

Publication

Received: 1 February 2011

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

Volume 13, issue 2 (2013)