{
  "id": "0912.3054",
  "version": "v1",
  "published": "2009-12-16T04:28:20.000Z",
  "updated": "2009-12-16T04:28:20.000Z",
  "title": "Properties of Bott manifolds and cohomological rigidity",
  "authors": [
    "Suyoung Choi",
    "Dong Youp Suh"
  ],
  "comment": "22 pages",
  "journal": "Algebr. Geom. Topol. 11(2), (2011), 1053--1076",
  "categories": [
    "math.AT"
  ],
  "abstract": "The cohomological rigidity problem for toric manifolds asks whether the cohomology ring of a toric manifold determines the topological type of the manifold. In this paper, we consider the problem with the class of one-twist Bott manifolds to get an affirmative answer to the problem. We also generalize the result to quasitoric manifolds. In doing so, we show that the twist number of a Bott manifold is well-defined and is equal to the cohomological complexity of the cohomology ring of the manifold. We also show that any cohomology Bott manifold is homeomorphic to a Bott manifold. All these results are also generalized to the case with $\\mathbb Z_{(2)}$-coefficients, where $\\mathbb Z_{(2)}$ is the localized ring at 2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-16T04:28:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57S25",
      "22F30"
    ],
    "keywords": [
      "properties",
      "toric manifolds asks",
      "cohomology bott manifold",
      "one-twist bott manifolds",
      "toric manifold determines"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.3054C"
    }
  }
}