{
  "id": "2407.10467",
  "version": "v1",
  "published": "2024-07-15T06:46:25.000Z",
  "updated": "2024-07-15T06:46:25.000Z",
  "title": "A lower bound of the crossing number of composite knots",
  "authors": [
    "Ruifeng Qiu",
    "Chao Wang"
  ],
  "comment": "46 pages, 45 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $c(K)$ denote the crossing number of a knot $K$ and let $K_1\\# K_2$ denote the connected sum of two oriented knots $K_1$ and $K_2$. It is a very old unsolved question that whether $c(K_1\\# K_2)=c(K_1)+c(K_2)$. In this paper we show that $c(K_1\\# K_2)> (c(K_1)+c(K_2))/16$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-15T06:46:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57N10"
    ],
    "keywords": [
      "crossing number",
      "lower bound",
      "composite knots",
      "old unsolved question"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}