Geodesic
The localization of orthogonal calculus with respect to homology
Taggart, Niall1
1 Mathematical Institute, Utrecht University, Utrecht, Netherlands
Algebraic and Geometric Topology, Tome 24 (2024) no. 3, pp. 1505-1549

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For a set of maps of based spaces S we construct a version of Weiss’s 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.

DOI : 10.2140/agt.2024.24.1505
Keywords: orthogonal calculus, Bousfield localization, homological localization, nullification, calculus of functors

Taggart, Niall 1

1 Mathematical Institute, Utrecht University, Utrecht, Netherlands 
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Taggart, Niall. The localization of orthogonal calculus with respect to homology. Algebraic and Geometric Topology, Tome 24 (2024) no. 3, pp. 1505-1549. doi: 10.2140/agt.2024.24.1505

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