{
  "id": "2107.03671",
  "version": "v1",
  "published": "2021-07-08T08:18:48.000Z",
  "updated": "2021-07-08T08:18:48.000Z",
  "title": "On the homology theory for the chromatic polynomials",
  "authors": [
    "Zipei Zhuang"
  ],
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "In \\cite{10.2140/agt.2005.5.1365}, Rong and Helme-Guizon defined a categorification for the chromatic polynomial $P_G(x)$ of graphs $G$, i.e. a homology theory $H^*(G)$ whose Euler characteristic equals $P_G(x)$. In this paper, we showed that the rational homoology $H^*(G;\\mathbb{Q})$ is supported in two lines, and develop an analogy of Lee's theory for Khovanov homology. In particular, we develop a new homology theory $H_{Lee}(G)$, and showed that there is a spectral sequence whose $E_2$ -term is isomorphic to $H^*(G)$ converges to $H_{Lee}(G)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-08T08:18:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homology theory",
      "chromatic polynomial",
      "euler characteristic equals",
      "rational homoology",
      "lees theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}