{
  "id": "2105.13416",
  "version": "v1",
  "published": "2021-05-27T19:37:26.000Z",
  "updated": "2021-05-27T19:37:26.000Z",
  "title": "Deformations of functions on surfaces",
  "authors": [
    "Sergiy Maksymenko"
  ],
  "comment": "41 page",
  "journal": "Proceedings of the Institute of Mathematics of NAS of Ukraine, 2020, vol 17, no. 2, pp. 150-199",
  "categories": [
    "math.GT",
    "math.AT",
    "math.DG",
    "math.DS"
  ],
  "abstract": "The paper contains a review on recent progress in the deformational properties of smooth maps from compact surfaces $M$ to a one-dimensional manifold $P$. It covers description of homotopy types of stabilizers and orbits of a large class of smooth functions on surfaces obtained by the author, E. Kudryavtseva, B. Feshchenko, I. Kuznietsova, Yu. Soroka, A. Kravchenko. We also present here a new direct proof of the fact that for generic Morse maps the connected components their orbits are homotopy equivalent to finite products of circles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-27T19:37:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J05",
      "57S05",
      "58B05"
    ],
    "keywords": [
      "deformations",
      "generic morse maps",
      "smooth maps",
      "compact surfaces",
      "one-dimensional manifold"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}