{
  "id": "2311.15256",
  "version": "v1",
  "published": "2023-11-26T10:00:55.000Z",
  "updated": "2023-11-26T10:00:55.000Z",
  "title": "On the $L_{\\infty}$-bialgebra structure of the rational homotopy groups $π_{*}(ΩΣY)\\otimes \\mathbb{Q}$",
  "authors": [
    "Samson Saneblidze"
  ],
  "comment": "7 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "We introduce the notion of an $L_{\\infty}$-bialgebra structure on a vector space. We show that the rational homotopy groups $\\pi_{*}(\\Omega \\Sigma Y)\\otimes \\mathbb{Q}$ admit such a structure for the loop space $\\Omega \\Sigma Y$ of a suspension $\\Sigma Y$ that characterizes $Y$ up to rational homotopy equivalence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-26T10:00:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P35",
      "55S05"
    ],
    "keywords": [
      "rational homotopy groups",
      "bialgebra structure",
      "rational homotopy equivalence",
      "vector space",
      "loop space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}