{
  "id": "2304.08043",
  "version": "v1",
  "published": "2023-04-17T07:57:24.000Z",
  "updated": "2023-04-17T07:57:24.000Z",
  "title": "Van Kampen-Flores theorem and Stiefel-Whitney classes",
  "authors": [
    "Daisuke Kishimoto",
    "Takahiro Matsushita"
  ],
  "comment": "8 pages",
  "categories": [
    "math.AT",
    "math.CO",
    "math.GT"
  ],
  "abstract": "The van Kampen-Flores theorem states that the $d$-skeleton of a $(2d+2)$-simplex does not embed into $\\mathbb{R}^{2d}$. We prove the van Kampen-Flores theorem for triangulations of manifolds satisfying a certain condition on their Stiefel-Whitney classes. In particular, we show that the $d$-skeleton of a triangulation of a $(2d+1)$-manifold with non-trivial total Stiefel-Whitney class does not embed into $\\mathbb{R}^{2d}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-17T07:57:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "van kampen-flores theorem states",
      "non-trivial total stiefel-whitney class",
      "triangulation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}