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arXiv · 2109.13806

The localization of orthogonal calculus with respect to homology

Niall Taggart
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Abstract

For a set of maps of based spaces $S$ we construct a version of Weiss' orthogonal calculus which depends only on the $S$-local homotopy type of the functor involved. We show that $S$-local homogeneous functors of degree $n$ are equivalent to levelwise $S$-local spectra with an action of the orthogonal group $O(n)$ via a zigzag of Quillen equivalences between appropriate model categories. Our theory specialises to homological localizations and nullifications at a based space. We give a variety of applications including a reformulation of the Telescope Conjecture in terms of our local orthogonal calculus and a calculus version of Postnikov sections. Our results also apply when considering the orthogonal calculus for functors which take values in spectra.

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Niall Taggart. 2021-09-28. The localization of orthogonal calculus with respect to homology. https://doi.org/10.2140/agt.2024.24.1505

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