{
  "id": "math/0301043",
  "version": "v1",
  "published": "2003-01-06T19:23:20.000Z",
  "updated": "2003-01-06T19:23:20.000Z",
  "title": "Algebraic structure of the space of homotopy classes of cycles and singular homology",
  "authors": [
    "Valery Dolotin"
  ],
  "comment": "6 pages LaTeX, 5 figures",
  "categories": [
    "math.AT",
    "math.KT"
  ],
  "abstract": "Described the algebraic structure on the space of homotopy classes of cycles with marked topological flags of disks. This space is a non-commutative monoid, with an Abelian quotient corresponding to the group of singular homologies $H_k(M)$. For the marked flag contracted to a point the multiplication becomes commutative and the subgroup of spherical cycles corresponds to the usual homotopy group $\\pi_k(M)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-01-06T19:23:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "algebraic structure",
      "homotopy classes",
      "singular homology",
      "usual homotopy group",
      "spherical cycles corresponds"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......1043D"
    }
  }
}