{
  "id": "2104.14880",
  "version": "v1",
  "published": "2021-04-30T10:09:08.000Z",
  "updated": "2021-04-30T10:09:08.000Z",
  "title": "Connected components of Isom($\\mathbb{H}^3$)-representations of non-orientable surfaces",
  "authors": [
    "Juan Luis Durán Batalla"
  ],
  "comment": "13 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $N_k$ denote the closed non-orientable surface of genus $k$. In this paper we study the behaviour of the `square map' from the group of isometries of hyperbolic 3-space to the subgroup of orientation preserving isometries. We show that there are $2^{k+1}$ connected components of representations of $\\pi_1(N_k)$ in Isom$(\\mathbb{H}^3)$, which are distinguished by the Stiefel-Whitney classes of the associated flat bundle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-30T10:09:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M05"
    ],
    "keywords": [
      "connected components",
      "representations",
      "orientation preserving isometries",
      "stiefel-whitney classes",
      "associated flat bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}