{
  "id": "2303.03333",
  "version": "v2",
  "published": "2023-03-06T18:05:09.000Z",
  "updated": "2023-08-23T21:25:36.000Z",
  "title": "LS-category and topological complexity of Milnor manifolds and corresponding generalized projective product spaces",
  "authors": [
    "Navnath Daundkar"
  ],
  "comment": "16 pages. Version 2: Theorem 3.2 has been modified, Theorem 3.5 has been added, typos fixed",
  "categories": [
    "math.AT"
  ],
  "abstract": "Milnor manifolds are a class of certain codimension-$1$ submanifolds of the product of projective spaces. In this paper, we study the LS-category and topological complexity of these manifolds. We determine the exact value of the LS-category and in many cases, the topological complexity of these manifolds. We also obtain tight bounds on the topological complexity of these manifolds. It is known that Milnor manifolds admit $\\mathbb{Z}_2$ and circle actions. We compute bounds on the equivariant LS-category and equivariant topological complexity of these manifolds. Finally, we describe the mod-$2$ cohomology rings of some generalized projective product spaces corresponding to Milnor manifolds and use this information to compute the bound on LS-category and topological complexity of these spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-08-23T21:25:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55M30",
      "55P15",
      "57N65"
    ],
    "keywords": [
      "topological complexity",
      "corresponding generalized projective product spaces",
      "ls-category",
      "projective product spaces corresponding",
      "milnor manifolds admit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}