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Rational Orthogonal Calculus

2015/11/16 by David Barnes, Barnes, David
Mathematics · Physics and Astronomy · #55N91 #55P42 #55P62 #55U35 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1511.05184

openalex publication_date 2015/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that one can use model categories to construct rational orthogonal calculus. That is, given a continuous functor from vector spaces to based spaces one can construct a tower of approximations to this functor depending only on the rational homology type of the input functor, whose layers are given by rational spectra with an action of O(n). By work of Greenlees and Shipley, we see that these layers are classified by torsion H^*(B SO(n))[O(n)/SO(n)]-modules.

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