{
  "id": "2003.13125",
  "version": "v1",
  "published": "2020-03-29T19:54:04.000Z",
  "updated": "2020-03-29T19:54:04.000Z",
  "title": "Estimate of number of simplices of triangulations of Lie groups",
  "authors": [
    "Haibao Duan",
    "Wacław Marzantowicz",
    "Xuezhi Zhao"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "We present estimates of number of simplices of given dimension of classical compact Lie groups. As in the previous work \\cite{GMP2} the approach is a combination of an estimate of number of vertices with a use of valuation of the covering type by cohomological argument of \\cite{GMP} and application of the recent versions of the Lower Bound Theorem of combinatorial topology. For the case of exceptional Lie groups we made a complete calculation using the description of their cohomology rings given by the first and third author. For infinite increasing series of Lie groups of growing dimension $d$ the rate of growth of number of simplices of highest dimension is given which extends onto the case of simplices of (fixed) codimension $d-i$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-29T19:54:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q15",
      "52B05",
      "57T10"
    ],
    "keywords": [
      "triangulations",
      "exceptional lie groups",
      "classical compact lie groups",
      "lower bound theorem",
      "combinatorial topology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}