Rational Orthogonal Calculus

David Barnes

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arXiv · 1511.05184

Rational Orthogonal Calculus

David Barnes

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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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David Barnes. 2017-03-15. Rational Orthogonal Calculus. https://arxiv.org/abs/1511.05184

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