{
  "id": "1812.03734",
  "version": "v1",
  "published": "2018-12-10T11:11:07.000Z",
  "updated": "2018-12-10T11:11:07.000Z",
  "title": "Boundary and Eisenstein Cohomology of $\\mr{SL}_3(\\Z)$",
  "authors": [
    "Jitendra Bajpai",
    "Günter Harder",
    "Ivan Horozov",
    "Matias Moya Giusti"
  ],
  "comment": "40 Pages, 1 Figure, 9 Tables",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this article, several cohomology spaces associated to the arithmetic groups $\\mr{SL}_3(\\Z)$ and $\\mr{GL}_3(\\Z)$ with coefficients in any highest weight representation $\\m_\\lambda$ have been computed, where $\\lambda$ denotes their highest weight. Consequently, we obtain detailed information of their Eisenstein cohomology with coefficients in $\\m_\\lambda$. When $\\m_\\lambda$ is not self dual, the Eisenstein cohomology coincides with the cohomology of the underlying arithmetic group with coefficients in $\\m_\\lambda$. In particular, for such a large class of representations we can explicitly describe the cohomology of these two arithmetic groups. We accomplish this by studying the cohomology of the boundary of the Borel-Serre compactification and their Euler characteristic with coefficients in $\\m_\\lambda$. At the end, we employ our study to discuss the existence of ghost classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-10T11:11:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arithmetic group",
      "coefficients",
      "highest weight representation",
      "eisenstein cohomology coincides",
      "euler characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}