{
  "id": "2505.04118",
  "version": "v1",
  "published": "2025-05-07T04:26:05.000Z",
  "updated": "2025-05-07T04:26:05.000Z",
  "title": "Coarse Geometry of Free Products of Metric Spaces",
  "authors": [
    "Qin Wang",
    "Jvbin Yao"
  ],
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "Recently, a notion of the free product $X \\ast Y$ of two metric spaces $X$ and $Y$ has been introduced by T. Fukaya and T. Matsuka. In this paper, we study coarse geometric permanence properties of the free product $X \\ast Y$. We show that if $X$ and $Y$ satisfy any of the following conditions, then $X \\ast Y$ also satisfies that condition: (1) they are coarsely embeddable into a Hilbert space or a uniformly convex Banach space; (2) they have Yu's Property A; (3) they are hyperbolic spaces. These generalize the corresponding results for discrete groups to the case of metric spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-07T04:26:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "metric spaces",
      "free product",
      "coarse geometry",
      "study coarse geometric permanence properties",
      "uniformly convex banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}