{
  "id": "1612.03837",
  "version": "v1",
  "published": "2016-12-12T18:37:10.000Z",
  "updated": "2016-12-12T18:37:10.000Z",
  "title": "On H-Spaces and a Congruence of Catalan Numbers",
  "authors": [
    "Tamar Friedmann",
    "John R. Harper"
  ],
  "comment": "15 pages; accepted for publication in Homology, Homotopy and Applications",
  "categories": [
    "math.CO",
    "math.AT",
    "math.NT"
  ],
  "abstract": "For $p$ an odd prime and $F$ the cyclic group of order $p$, we show that the number of conjugacy classes of embeddings of $F$ in $SU(p)$ such that no element of $F$ has 1 as an eigenvalue is $(1+C_{p-1})/p$, where $C_{p-1}$ is a Catalan number. We prove that the only coset space $SU(p)/F$ that admits a $p$-local $H$-structure is the classical Lie group $PSU(p)$. We also show that $SU(4)/\\mathbb Z_3$, where $\\mathbb Z_3$ is embedded off the center of $SU(4)$, is a novel example of an $H$-space, even globally. We apply our results to the study of homotopy classes of maps from $BF$ to $BSU(n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-12T18:37:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "55P45",
      "05E15",
      "11A07",
      "11B50"
    ],
    "keywords": [
      "catalan number",
      "congruence",
      "coset space",
      "cyclic group",
      "odd prime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}