{
  "id": "1207.7249",
  "version": "v3",
  "published": "2012-07-31T14:06:35.000Z",
  "updated": "2013-06-17T11:33:10.000Z",
  "title": "Non-existence of tight neighborly manifolds with $β_1=2$",
  "authors": [
    "Nitin Singh"
  ],
  "comment": "8 pages. arXiv admin note: text overlap with arXiv:1102.0856, arXiv:1207.5599 by other authors",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "For $d\\geq 2$, Walkup's class $\\Kd$ consists of the $d$-dimensional simplicial complexes whose vertex-links are stacked $(d-1)$-spheres. Recently Lutz, Sulanke and Swartz have shown that all $\\mathbb{F}$-orientable triangulated $d$-manifolds satisfy the inequality $\\binom{f_0-d-1}{2} \\geq \\binom{d+2}{2}\\beta_1$ for $d\\geq 3$. They call a $d$-manifold \\emph{tight neighborly} if it attains the equality in the bound. For $d\\geq 4$, tight neighborly $d$-manifolds are precisely the 2-neighborly members of $\\Kd$. In this paper we show that there does not exist any tight neighborly $d$-manifold with $\\beta_1=2$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-06-17T11:33:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q15",
      "57R05"
    ],
    "keywords": [
      "tight neighborly manifolds",
      "non-existence",
      "dimensional simplicial complexes",
      "walkups class",
      "manifolds satisfy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.7249S"
    }
  }
}