{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "6PDWHWQQ11"
    },
    {
      "field": "uses",
      "target": "AWZHWFBN53"
    },
    {
      "field": "uses",
      "target": "C1KY6MAW0J"
    },
    {
      "field": "uses",
      "target": "V9HGTHC7DE"
    },
    {
      "field": "defines",
      "target": "XDYMCB41NG"
    }
  ],
  "body": "\n## Summary\n\nA section of a vector bundle chooses one vector in the fiber over each point of the base.\nThe choice varies smoothly with the point.\nVector fields are sections of the tangent bundle, and differential forms are sections of bundles of alternating forms.\nThe sections of a vector bundle form a vector space, and in fact a module over the ring of smooth functions on the base.\nMany objects of geometry and physics, such as fields in gauge theory, are sections of suitable bundles.\n\n## Explanations\n\n### L1 human\n\nA vector bundle attaches a vector space to each point of a space.\nA section picks one vector from each of these spaces, without jumps.\nWind directions on the surface of the Earth form a section of the tangent bundle of the sphere: at each place you get an arrow tangent to the surface.\nOn a trivial bundle $M \\times \\R^k$, a section is just a smooth function from $M$ to $\\R^k$.\n",
  "commit": "5fc425f97f1f6b11da5892c2948ef8c5d8805665",
  "front": {
    "kind": "concept",
    "msc": [
      "55R25",
      "58A05"
    ],
    "name": "Section of a vector bundle",
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Section_(fiber_bundle)"
      }
    ],
    "tag": "WWX7H5W1RP"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/WWX7H5W1RP/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/WWX7H5W1RP.md",
  "msc": [
    "55R25",
    "58A05"
  ],
  "name": "Section of a vector bundle",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/WWX/WWX7H5W1RP.md",
  "status": null,
  "tag": "WWX7H5W1RP",
  "uri": "m2://WWX7H5W1RP",
  "url": "https://math2.tamnd.com/wiki/section-of-a-vector-bundle/",
  "writing": {
    "tag": "WWX7H5W1RP",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}