{
  "id": "1608.00960",
  "version": "v1",
  "published": "2016-08-02T19:45:34.000Z",
  "updated": "2016-08-02T19:45:34.000Z",
  "title": "Morin singularities of coframes and frames",
  "authors": [
    "Camila M. Ruiz"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "Inspired by the properties of an $n$-frame of gradients $(\\nabla f_1, \\ldots, \\nabla f_n)$ of a Morin map $f:M\\rightarrow\\mathbb{R}^n$, with $\\dim M\\geq n$, we introduce the notion of Morin singularities in the context of singular $n$-coframes and singular $n$-frames. We also study the singularities of generic 1-forms associated to a Morin $n$-coframe, in order to generalize a result of T. Fukuda [4, Theorem 1], which establishes a modulo 2 congruence between the Euler characteristic of a compact manifold $M$ and the Euler characteristics of the singular sets of a Morin map defined on $M$, to the case of Morin $n$-coframes and Morin $n$-frames.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-02T19:45:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "morin singularities",
      "morin map",
      "euler characteristic",
      "compact manifold",
      "singular sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}