{
  "id": "2106.09195",
  "version": "v1",
  "published": "2021-06-17T01:11:05.000Z",
  "updated": "2021-06-17T01:11:05.000Z",
  "title": "On the Classifying Space for Commutativity in $U(3)$",
  "authors": [
    "Santanil Jana"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "For a Lie group $G$, let $B_{com} G$ be the classifying space for commutativity. Let $E_{com} G$ be the total space of the principal $G$-bundle associated to $B_{com} G$. In this article, we present a computation of the cohomology of $E_{com} U(3)$ using the spectral sequence associated to a homotopy colimit. As a part of our computation we will also compute the integral cohomology of $U(3)/N(T)$ and $(U(3)/T) \\times_{\\Sigma_3} (U(3)/T)$ where $T$ is a maximal torus of $U(3)$ with normalizer $N(T)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-17T01:11:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R40",
      "55R20"
    ],
    "keywords": [
      "classifying space",
      "commutativity",
      "maximal torus",
      "lie group",
      "integral cohomology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}