{
  "id": "2303.11227",
  "version": "v1",
  "published": "2023-03-20T16:08:12.000Z",
  "updated": "2023-03-20T16:08:12.000Z",
  "title": "The compact-open topology on the diffeomorphism or homeomorphism group of a smooth manifold without boundary is minimal in almost all dimensions",
  "authors": [
    "J. de la Nuez González"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that for any connected smooth manifold $M$ of dimension different from $3$ the restriction of the compact-open topology to the diffeomorphism group of $M$ is minimal, i.e. the group does not admit a strictly coarser Hausdorff group topology. This implies the minimality of the compact-open topology on the homeomorphism group of $M$ in all dimensions different from $3$ and $4$. In those cases for which in addition to all of this automatic continuity is known to hold, such as when $M$ is closed, one can conclude that the compact-open topology is the unique separable Hausdorff group topology on the homeomorphism group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-20T16:08:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Rxx",
      "57Sxx"
    ],
    "keywords": [
      "compact-open topology",
      "homeomorphism group",
      "smooth manifold",
      "diffeomorphism",
      "strictly coarser hausdorff group topology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}