{
  "id": "math/0611803",
  "version": "v1",
  "published": "2006-11-27T01:43:00.000Z",
  "updated": "2006-11-27T01:43:00.000Z",
  "title": "Homology of dihedral quandles",
  "authors": [
    "Maciej Niebrzydowski",
    "Jozef H. Przytycki"
  ],
  "comment": "21 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "We solve the conjecture by R. Fenn, C. Rourke and B. Sanderson that the rack homology of dihedral quandles satisfies H_3^R(R_p) = Z \\oplus Z_p for p odd prime. We also show that H_n^R(R_p) contains Z_p for n>2. Furthermore, we show that the torsion of H_n^R(R_3) is annihilated by 3. We also prove that the quandle homology H_4^Q(R_p) contains Z_p for p odd prime. We conjecture that for n>1 quandle homology satisfies: H_n^Q(R_p) = Z_p^{f_n}, where f_n are \"delayed\" Fibonacci numbers, that is, f_n = f_{n-1} + f_{n-3} and f(1)=f(2)=0, f(3)=1. Our paper is the first step in approaching this conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-11-27T01:43:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N35",
      "57M25"
    ],
    "keywords": [
      "odd prime",
      "conjecture",
      "quandle homology satisfies",
      "dihedral quandles satisfies",
      "first step"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11803N"
    }
  }
}