{
  "id": "2403.17964",
  "version": "v1",
  "published": "2024-03-14T18:47:11.000Z",
  "updated": "2024-03-14T18:47:11.000Z",
  "title": "Quantifying separability in RAAGs via representations",
  "authors": [
    "Olga Kharlampovich",
    "Alina Vdovina"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:2303.03644",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We answer the question asked by Louder, McReynolds and Patel, and prove the following statement. Let L be a RAAG, H a word quasiconvex subgroup of L, then there is a finite dimensional representation of L that separates the subgroup H in the induced Zariski topology. As a corollary, we establish a polynomial upper bound on the size of the quotients used to separate H in L. This implies the same statement for a virtually special group L and, in particular, a fundamental groups of a hyperbolic 3-manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-14T18:47:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E26",
      "20C99"
    ],
    "keywords": [
      "quantifying separability",
      "word quasiconvex subgroup",
      "finite dimensional representation",
      "polynomial upper bound",
      "induced zariski topology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}