{
  "id": "1806.00010",
  "version": "v1",
  "published": "2018-05-31T18:00:01.000Z",
  "updated": "2018-05-31T18:00:01.000Z",
  "title": "Topological structure of spaces of stability conditions and topological Fukaya type categories",
  "authors": [
    "Yu Qiu"
  ],
  "comment": "This survey is contributed to the proceedings of the first annual meeting of ICCM",
  "categories": [
    "math.RT",
    "math.AG",
    "math.GT"
  ],
  "abstract": "This is a survey on two closely related subjects. First, we review the study of topological structure of `finite type' components of spaces of Bridgeland's stability conditions on triangulated categories. The key is to understand Happel-Reiten-Smalo tilting as tiling of cells. Second, we review topological realizations of various Fukaya type categories, namely cluster/Calabi-Yau and derived categories from surfaces. The corresponding spaces of stability conditions are of `tame' nature and can be realized as moduli spaces of quadratic differentials due to Bridgeland-Smith and Haiden-Katzarkov-Kontsevich.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-31T18:00:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topological fukaya type categories",
      "topological structure",
      "bridgelands stability conditions",
      "quadratic differentials",
      "finite type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}