{
  "id": "2105.04426",
  "version": "v1",
  "published": "2021-05-10T14:38:05.000Z",
  "updated": "2021-05-10T14:38:05.000Z",
  "title": "Exponential growth in the rational homology of free loop spaces and in torsion homotopy groups",
  "authors": [
    "Ruizhi Huang",
    "Stephen Theriault"
  ],
  "comment": "12 pages; comments are very welcome",
  "categories": [
    "math.AT"
  ],
  "abstract": "Using integral methods we recover and generalize some results by F\\'{e}lix, Halperin and Thomas on the growth of the rational homology groups of free loop spaces, and obtain a new family of spaces whose $p$-torsion in homotopy groups grows exponentially and satisfies Moore's Conjecture for all but finitely many primes. In view of the results, we conjecture that there should be a strong connection between exponential growth in the rational homotopy groups and the $p$-torsion homotopy groups for any prime $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-10T14:38:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P35",
      "55P62"
    ],
    "keywords": [
      "free loop spaces",
      "torsion homotopy groups",
      "exponential growth",
      "rational homotopy groups",
      "rational homology groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}