{
  "id": "2109.13806",
  "version": "v3",
  "published": "2021-09-28T15:34:24.000Z",
  "updated": "2022-12-07T10:25:51.000Z",
  "title": "The localization of orthogonal calculus with respect to homology",
  "authors": [
    "Niall Taggart"
  ],
  "comment": "42 pages, 2 figures. Comments welcome! v2: Largely rewritten the entire article, main results remain unchanged. v.3 Accepted for publication in Algebraic & Geometric Topology",
  "categories": [
    "math.AT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2022-12-07T10:25:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "localization",
      "local homotopy type",
      "appropriate model categories",
      "local orthogonal calculus",
      "postnikov sections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}