Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2109.13806 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914862828879872 |
|---|---|
| author | Taggart, Niall |
| author_facet | Taggart, Niall |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_13806 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The localization of orthogonal calculus with respect to homology Taggart, Niall Algebraic Topology 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. |
| title | The localization of orthogonal calculus with respect to homology |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2109.13806 |