{
  "id": "1607.05056",
  "version": "v1",
  "published": "2016-07-18T13:20:03.000Z",
  "updated": "2016-07-18T13:20:03.000Z",
  "title": "Mixing, malnormal subgroups and cohomology in degree one",
  "authors": [
    "Antoine Gournay"
  ],
  "comment": "35 pages",
  "categories": [
    "math.GR",
    "math.GT",
    "math.RT"
  ],
  "abstract": "The aim of the current paper is to explore the implications on the group $G$ of the non-vanishing of the cohomology in degree one of one of its representation $\\pi$, given some mixing conditions on $\\pi$. In one direction, harmonic cocycles are used to show that the FC-centre should be finite (for mildly mixing unitary representations). Next, for any subgroup $H<G$, $H$ will either be \"small\", almost-malnormal or $\\pi_{|H}$ also has non-trivial cohomology in degree one (in this statement, \"small\", reduced vs unreduced cohomology and unitary vs generic depend on the mixing condition). The notion of q-normal subgroups is an important ingredient of the proof and results on the vanishing of the reduced $\\ell^p$-cohomology in degree one are obtained as an intermediate step.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-18T13:20:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "malnormal subgroups",
      "mixing condition",
      "current paper",
      "q-normal subgroups",
      "non-trivial cohomology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}