{
  "id": "2302.00468",
  "version": "v1",
  "published": "2023-02-01T14:29:29.000Z",
  "updated": "2023-02-01T14:29:29.000Z",
  "title": "LS-category and Topological complexity of several families of fibre bundles",
  "authors": [
    "Navnath Daundkar",
    "Soumen Sarkar"
  ],
  "comment": "18 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "In this paper, we study upper bounds for the topological complexity of the total spaces of some classes of fibre bundles. We calculate a tight upper bound for the topological complexity of an $n$-dimensional Klein bottle. We also compute the exact value of the topological complexity of $2$ and $3$-dimensional Klein bottles. We describe the cohomology rings of several classes of generalized projective product spaces with $\\mathbb{Z}_2$-coefficients. Then we study the LS-category and topological complexity of infinite families of generalized projective product spaces. We also compute the exact value of these invariants in many specific cases. We calculate the equivariant LS-category and equivariant topological complexity of several product spaces equipped with $\\mathbb{Z}_2$-action.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-01T14:29:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55M30",
      "55P15",
      "57N65"
    ],
    "keywords": [
      "topological complexity",
      "fibre bundles",
      "ls-category",
      "generalized projective product spaces",
      "dimensional klein bottle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}