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arXiv · 1101.4099

Model Categories for Orthogonal Calculus

David Barnes·Peter Oman
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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 of Weiss. As an application, we develop a variant of orthogonal calculus by replacing topological spaces with orthogonal spectra.

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David Barnes, Peter Oman. 2012-08-10. Model Categories for Orthogonal Calculus. https://doi.org/10.2140/agt.2013.13.959

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