{
  "id": "math/0203179",
  "version": "v2",
  "published": "2002-03-18T17:18:39.000Z",
  "updated": "2003-01-06T15:52:59.000Z",
  "title": "Characterization of Y_2-equivalence for homology cylinders",
  "authors": [
    "Gwenael Massuyeau",
    "Jean-Baptiste Meilhan"
  ],
  "comment": "29 pages with 8 figures; a few minor improvements",
  "journal": "J. Knot Th. Ramifications 12:4 (2003) 493-522",
  "categories": [
    "math.GT"
  ],
  "abstract": "For S a compact connected oriented surface, we consider homology cylinders over S: these are homology cobordisms with an extra homological triviality condition. When considered up to Y_2-equivalence, which is a surgery equivalence relation arising from the Goussarov-Habiro theory, homology cylinders form an Abelian group. In this paper, when S has one or zero boundary component, we define a surgery map from a certain space of graphs to this group. This map is shown to be an isomorphism, with inverse given by some extensions of the first Johnson homomorphism and Birman-Craggs homomorphisms.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-01-06T15:52:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N10",
      "57M27"
    ],
    "keywords": [
      "characterization",
      "first johnson homomorphism",
      "extra homological triviality condition",
      "zero boundary component",
      "homology cylinders form"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......3179M"
    }
  }
}