{
  "id": "1906.00737",
  "version": "v1",
  "published": "2019-06-03T12:21:52.000Z",
  "updated": "2019-06-03T12:21:52.000Z",
  "title": "The Hard Lefschetz Theorem for PL spheres",
  "authors": [
    "Karim Adiprasito",
    "Johanna K. Steinmeyer"
  ],
  "comment": "8 pages. arXiv admin note: text overlap with arXiv:1812.10454",
  "categories": [
    "math.CO",
    "math.AC",
    "math.AG",
    "math.GT"
  ],
  "abstract": "We provide a simpler proof of the hard Lefschetz Theorem for face rings of PL spheres. This simplifies the reasoning for an important special case of the main result of the first author in [arxiv:1812.10454], and already implies the McMullen g-conjecture for PL spheres, as well as the Gr\\\"unbaum-Kalai-Sarkaria conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-03T12:21:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E45",
      "13F55",
      "32S50",
      "14M25",
      "05E40",
      "52B70",
      "57Q15"
    ],
    "keywords": [
      "hard lefschetz theorem",
      "pl spheres",
      "important special case",
      "mcmullen g-conjecture",
      "face rings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}