{
  "id": "2211.08409",
  "version": "v1",
  "published": "2022-11-15T18:47:21.000Z",
  "updated": "2022-11-15T18:47:21.000Z",
  "title": "Colored sl(N) homology and SU(N) representations of the trefoil",
  "authors": [
    "Joshua Wang"
  ],
  "comment": "54 pages",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "We show that the colored sl(N) homology of the trefoil labeled by an exterior power of the defining representation is isomorphic to the cohomology of a closed manifold naturally associated to the trefoil. This manifold is the set of homomorphisms from the fundamental group of the complement of the trefoil to SU(N) that send meridians to a particular conjugacy class depending on the label. We also prove the analogous isomorphisms for the Hopf link. These isomorphisms suggest a close relationship between colored sl(N) homology and instanton Floer homology with gauge group SU(N).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-15T18:47:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "colored sl",
      "representation",
      "gauge group su",
      "instanton floer homology",
      "exterior power"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 54,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}