{
  "id": "0810.0365",
  "version": "v1",
  "published": "2008-10-02T09:01:33.000Z",
  "updated": "2008-10-02T09:01:33.000Z",
  "title": "On o-minimal homotopy groups",
  "authors": [
    "Elias Baro",
    "Margarita Otero"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We work over an o-minimal expansion of a real closed field. The o-minimal homotopy groups of a definable set are defined naturally using definable continuous maps. We prove that any two semialgebraic maps which are definably homotopic are also semialgebraically homotopic. This result together with the study of semialgebraic homotopy done by H. Delfs and M. Knebusch allows us to develop an o-minimal homotopy theory. In particular, we obtain o-minimal versions of the Hurewicz theorems and the Whitehead theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-02T09:01:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C64",
      "14P10",
      "55Q99"
    ],
    "keywords": [
      "o-minimal homotopy groups",
      "o-minimal homotopy theory",
      "o-minimal expansion",
      "hurewicz theorems",
      "o-minimal versions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.0365B"
    }
  }
}