Model categories for orthogonal calculus

Barnes, David¹ ; Oman, Peter²

¹Pure Mathematics Research Centre, David Bates Building, Queen’s University, Belfast BT7 1NN, UK
²Department of Mathematics, Southeast Missouri State University, One University Plaza, Cape Girardeau, MO 63701, USA

Algebraic and Geometric Topology, Tome 13 (2013) no. 2, pp. 959-999

Résumé

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.

Détail

DOI : 10.2140/agt.2013.13.959

Classification : 55P42, 55P91, 55U35
Keywords: orthogonal calculus, model categories, spectra, orthogonal spectra

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