{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "2SFM73YET0"
    },
    {
      "field": "uses",
      "target": "FZH5T5340Q"
    },
    {
      "field": "specializes",
      "target": "AGZSZW7GYE"
    },
    {
      "field": "defines",
      "target": "BW8X6DXTHG"
    },
    {
      "field": "about",
      "target": "FZH5T5340Q"
    }
  ],
  "body": "\n## Summary\n\nThe connected sum of two connected $n$-manifolds is formed by cutting a small open ball out of each.\nThe two resulting boundary spheres are then glued together.\nThe result is again a connected $n$-manifold, written $M \\# N$.\nThe operation is the basic way to build new manifolds from old ones.\nThe classification of surfaces and the prime decomposition of $3$-manifolds are stated in terms of it.\n\n## Explanations\n\n### L1 human\n\nTake two surfaces, for example two doughnut surfaces.\nPunch a small round hole in each.\nJoin the two holes with a short tube, or simply sew the edges of the holes together.\nThe result is one surface with two handles, the surface of a pretzel with two holes.\nTaking the connected sum with a sphere changes nothing, since the sphere with a hole is just a disk that plugs the hole again.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "kind": "concept",
    "msc": [
      "57N99",
      "57R65"
    ],
    "name": "Connected sum",
    "same_as": {
      "wikidata": "Q1890389",
      "wikipedia": "Connected sum"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Connected_sum"
      }
    ],
    "tag": "Y0K0K5NGWW"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/Y0K0K5NGWW/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/Y0K0K5NGWW.md",
  "msc": [
    "57N99",
    "57R65"
  ],
  "name": "Connected sum",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/Y0K/Y0K0K5NGWW.md",
  "status": null,
  "tag": "Y0K0K5NGWW",
  "uri": "m2://Y0K0K5NGWW",
  "url": "https://math2.tamnd.com/wiki/connected-sum/",
  "writing": {
    "tag": "Y0K0K5NGWW",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}