{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "3JAY4V0GAF"
    },
    {
      "field": "uses",
      "target": "56YF8W9NXP"
    },
    {
      "field": "uses",
      "target": "E1E5ABP89W"
    },
    {
      "field": "uses",
      "target": "HM23BV561Z"
    },
    {
      "field": "uses",
      "target": "NHY3HE7RCN"
    },
    {
      "field": "uses",
      "target": "TEG1ZX1AGJ"
    },
    {
      "field": "uses",
      "target": "WEGT4EZCX2"
    },
    {
      "field": "about",
      "target": "56YF8W9NXP"
    },
    {
      "field": "about",
      "target": "E1E5ABP89W"
    },
    {
      "field": "about",
      "target": "HM23BV561Z"
    },
    {
      "field": "defines",
      "target": "WTRPSJKAZH"
    }
  ],
  "body": "\n## Summary\n\nTwo closed manifolds of the same dimension are cobordant if together they form the boundary of a compact manifold of one dimension more.\nCobordism is an equivalence relation, much coarser than diffeomorphism, and its classes form groups under disjoint union.\nThe unoriented groups, and the [[cobordism ring|C02WQY819R]] they form under products, were computed by René Thom through the [[Thom spaces|5MNYT3AFPH]] of universal bundles.\nCobordism links differential topology with stable homotopy theory, and its variants, oriented, complex or framed, are generalized homology theories.\n\n## Explanations\n\n### L1 human\n\nImagine two closed surfaces as the two ends of a solid piece; the piece is a cobordism between them.\nA circle and a pair of circles are cobordant: a pair of pants has one waist and two leg openings, all circles.\nA single circle is the boundary of a disc, so it is cobordant to the empty manifold.\nCobordism ignores many details of shape and keeps only what survives such sweeping.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "kind": "concept",
    "msc": [
      "57R75",
      "55N22"
    ],
    "name": "Cobordism",
    "same_as": {
      "wikidata": "Q2546666",
      "wikipedia": "Cobordism"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Cobordism"
      }
    ],
    "tag": "T8BVGPPSZP"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/T8BVGPPSZP/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/T8BVGPPSZP.md",
  "msc": [
    "57R75",
    "55N22"
  ],
  "name": "Cobordism",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/T8B/T8BVGPPSZP.md",
  "status": null,
  "tag": "T8BVGPPSZP",
  "uri": "m2://T8BVGPPSZP",
  "url": "https://math2.tamnd.com/wiki/cobordism/",
  "writing": {
    "tag": "T8BVGPPSZP",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}