{
  "id": "math/0612152",
  "version": "v3",
  "published": "2006-12-06T13:25:29.000Z",
  "updated": "2008-07-28T11:50:41.000Z",
  "title": "Cobordism of singular maps",
  "authors": [
    "András Szűcs"
  ],
  "comment": "Revised version, some parts were excluded, some parts are explained in greater detail",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "We prove a conjecture due to M. Kazarian, connecting two classifying spaces in singularity theory. These spaces are: - Kazarian's space (generalizing Vassiliev's algebraic complex and) showing which cohomology classes are represented by singularity strata. - Author's space $X_\\tau$ giving homotopy representation of cobordisms of singular maps with a given list of allowed singularities \\cite{R--Sz}. As a consequence we obtain the ranks of cobordism groups of singular maps with a given list of allowed singularities, and also their $p$-torsion parts for big primes $p.$ Further we give complete answer to the problem of elimination of singularities by cobordisms. Obtain very clear homotopical description of the classifying space $X_\\tau.$ We reveal some connection of the torsion parts of these cobordism groups to the stable homotopy groups of spheres and values of Thom polynomials.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-07-28T11:50:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R45",
      "55P42"
    ],
    "keywords": [
      "singular maps",
      "cobordism groups",
      "torsion parts",
      "generalizing vassilievs algebraic complex",
      "classifying space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12152S"
    }
  }
}