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  "body": "\n## Summary\n\nThe holonomy groupoid of a [[foliation|98HTB7MSPX]] is a [[Lie groupoid|HNVW0E732J]] whose objects are the points of the manifold.\nIts arrows are paths inside leaves, where two paths count as equal when they have the same holonomy.\nIts orbits are the leaves, and its isotropy groups are the holonomy groups of the leaves.\nIt replaces the leaf space, which is often a badly behaved topological space, by a smooth object.\nIt is the starting point of the noncommutative geometry of foliations, through its convolution algebra.\n\n## Explanations\n\n### L1 human\n\nA foliation cuts a manifold into leaves, like the pages of a book, but the leaves can wind around in complicated ways.\nTo compare two points of the same leaf one walks from one to the other inside the leaf.\nWalking along a path also drags nearby leaves along, and the way they are moved is the holonomy of the path.\nThe holonomy groupoid has an arrow for each way of walking from one point to another.\nTwo walks count as the same when they move nearby leaves in the same way.\nFor the foliation of the plane by horizontal lines, there is exactly one arrow between two points on the same line and none between points on different lines.\n",
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  "name": "Holonomy groupoid of a foliation",
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