{
  "id": "1602.05982",
  "version": "v1",
  "published": "2016-02-18T21:37:36.000Z",
  "updated": "2016-02-18T21:37:36.000Z",
  "title": "A new proof of a theorem of Dutertre and Fukui on Morin singularities",
  "authors": [
    "Camila M. Ruiz"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "In [2], N.Dutertre and T. Fukui used Viro's integral calculus to study the topology of stable maps $f:M\\rightarrow N$ between two smooth manifolds $M$ and $N$. They also discussed several applications to Morin maps. In particular, in Theorem 6.2 [2], they show an equality relating the Euler characteristic of a compact manifold $M$ and the Euler characteristic of the singular sets of a Morin map defined on $M$. In this paper we show how Morse theory for manifolds with boundary can be applied to the study of the singular sets of a Morin map in order to obtain a new proof of Dutertre-Fukui's Theorem when $N=\\mathbb{R}^n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-18T21:37:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "morin singularities",
      "morin map",
      "euler characteristic",
      "singular sets",
      "viros integral calculus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160205982R"
    }
  }
}