{
  "id": "2411.16716",
  "version": "v1",
  "published": "2024-11-22T22:15:35.000Z",
  "updated": "2024-11-22T22:15:35.000Z",
  "title": "Equivalence of different definitions of higher $ρ$ invariants",
  "authors": [
    "Hongzhi Liu",
    "Zhizhang Xie",
    "Guoliang Yu"
  ],
  "comment": "28 pages",
  "categories": [
    "math.AT",
    "math.OA"
  ],
  "abstract": "For each orientation-preserving homotopy equivalence between two closed oriented smooth manifolds, there are mainly two different approaches to the higher $\\rho$ invariant associated to this homotopy equivalence. In this article, we show that these two definitions of the higher $\\rho$ invariant are equivalent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-22T22:15:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "definitions",
      "orientation-preserving homotopy equivalence",
      "closed oriented smooth manifolds",
      "approaches"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}