Model Categories for Orthogonal Calculus

Details Model Categories for Orthogonal Calculus Model Categories for Orthogonal Calculus

2011-01-21

arxiv.org/abs/1101.4099v2

Mathematics

Algebraic Topology

34 pages, major rewrite from previous version, classification of homogeneous functors is now a Quillen equivalence

Scientific paper

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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