{
  "id": "2104.04941",
  "version": "v1",
  "published": "2021-04-11T07:26:03.000Z",
  "updated": "2021-04-11T07:26:03.000Z",
  "title": "Fock--Goncharov coordinates for semisimple Lie groups",
  "authors": [
    "S. Gilles"
  ],
  "comment": "Ph.D. Thesis",
  "categories": [
    "math.GT"
  ],
  "abstract": "Fock and Goncharov introduced cluster ensembles, providing a framework for coordinates on varieties of surface representations into Lie groups, as well as a complete construction for groups of type $A_n$. Later, Zickert, Le, and Ip described, using differing methods, how to apply this framework for other Lie group types. Zickert also showed that this framework applies to triangulated $3$-manifolds. We present a complete, general construction, based on work of Fomin and Zelevinsky. In particular, we complete the picture for the remaining cases: Lie groups of types $F_4$, $E_6$, $E_7$, and $E_8$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-11T07:26:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semisimple lie groups",
      "fock-goncharov coordinates",
      "lie group types",
      "surface representations",
      "complete construction"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}