{
  "id": "1706.05050",
  "version": "v1",
  "published": "2017-06-15T19:13:13.000Z",
  "updated": "2017-06-15T19:13:13.000Z",
  "title": "Topology of Functions with Isolated Critical Points on the Boundary of a 2-dimensional Manifold",
  "authors": [
    "Bohdana Hladysh",
    "Aleksandr Prishlyak"
  ],
  "comment": "15 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "This paper focuses on the problem of topological equivalence of functions with isolated critical points on the boundary of a compact surface $M$ which are also isolated critical points of their restrictions to the boundary. This class of functions we denote by $\\Omega(M).$ Firstly, we've obtained the topological classification of above--mentioned functions in some neighborhood of their critical points. Secondly, we've constructed a chord diagram from the neighborhood of a critical level. Also the minimum number of critical points of such functions is being considered. And finally, the criterion of global topological equivalence of functions which belong to the $\\Omega(M)$ and have three critical points has been developed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-15T19:13:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R45",
      "57R70"
    ],
    "keywords": [
      "isolated critical points",
      "compact surface",
      "paper focuses",
      "neighborhood",
      "chord diagram"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}