{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "2VD7GR64JJ"
    },
    {
      "field": "uses",
      "target": "4RPERPNBK1"
    },
    {
      "field": "uses",
      "target": "5SY318V6S3"
    },
    {
      "field": "uses",
      "target": "7DM2KSS2DB"
    },
    {
      "field": "uses",
      "target": "D7K7YB52MM"
    },
    {
      "field": "about",
      "target": "7DM2KSS2DB"
    }
  ],
  "body": "\n## Summary\n\nThe suspension $SX$ of a topological space $X$ is the cylinder $X \\times [0, 1]$ with each end collapsed to its own point.\nIt looks like two cones on $X$ glued along their bases.\nThe suspension of the $n$-sphere is the $(n+1)$-sphere, and suspension shifts reduced homology up by one degree.\nIt is a basic construction in algebraic topology and stable homotopy theory.\n\n## Explanations\n\n### L1 human\n\nTake the space $X$ and stretch it into a tube $X \\times [0, 1]$.\nThen pinch the whole bottom end to one point and the whole top end to another point.\nThe space now hangs between a south pole and a north pole.\nFor example, the suspension of two points is a circle: each point becomes a path from the south pole to the north pole.\nThe suspension of a circle is a sphere, like a globe with its meridians.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "kind": "concept",
    "msc": [
      "55P40",
      "54B15"
    ],
    "name": "Suspension",
    "same_as": {
      "wikidata": "Q1307987",
      "wikipedia": "Suspension (topology)"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Suspension_(topology)"
      }
    ],
    "specializes": [
      "0CQHFPGJ45"
    ],
    "tag": "Q7RFNJH76Q"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/Q7RFNJH76Q/",
  "links": [
    {
      "field": "specializes",
      "target": "0CQHFPGJ45"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/Q7RFNJH76Q.md",
  "msc": [
    "55P40",
    "54B15"
  ],
  "name": "Suspension",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/Q7R/Q7RFNJH76Q.md",
  "status": null,
  "tag": "Q7RFNJH76Q",
  "uri": "m2://Q7RFNJH76Q",
  "url": "https://math2.tamnd.com/wiki/suspension/",
  "writing": {
    "tag": "Q7RFNJH76Q",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}