{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "R8PE771DDE"
    }
  ],
  "body": "\n## Summary\n\nThe linking number of two disjoint oriented closed curves in $\\R^3$ is an integer that counts how many times one curve winds around the other.\nIt does not change when the curves move without crossing each other, so it is an invariant of two-component [[links|1A5WRCNTM3]].\nIt can be read off a diagram, computed by a homology class, or given by the Gauss double integral.\n\n## Explanations\n\n### L1 human\n\nTake two closed loops of string in space that do not touch.\nThe linking number says how many times the first loop goes through the second, counted with a sign for the direction.\nTwo separate rings that can be pulled apart have linking number $0$.\nTwo rings hooked once, as in a chain, have linking number $1$ or $-1$, depending on the chosen directions.\nYou cannot unhook the rings without cutting one of them, and the number shows this.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "kind": "concept",
    "msc": [
      "57K10",
      "55M25"
    ],
    "name": "Linking number",
    "same_as": {
      "wikidata": "Q2000614",
      "wikipedia": "Linking number"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Linking_number"
      }
    ],
    "tag": "SFJ329YB9F"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/SFJ329YB9F/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/SFJ329YB9F.md",
  "msc": [
    "57K10",
    "55M25"
  ],
  "name": "Linking number",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/SFJ/SFJ329YB9F.md",
  "status": null,
  "tag": "SFJ329YB9F",
  "uri": "m2://SFJ329YB9F",
  "url": "https://math2.tamnd.com/wiki/linking-number/",
  "writing": {
    "tag": "SFJ329YB9F",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}