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  "body": "\n## Summary\n\nA foliation of a manifold is a decomposition of it into disjoint connected submanifolds of one fixed dimension, the leaves.\nLocally the leaves fit together like the parallel slices $\\R^p \\times \\set{y}$ of $\\R^p \\times \\R^q$.\nFoliations arise from integrable plane fields by the [[Frobenius theorem|5Q4BHBFXJY]] and from submersions.\nThey also arise from locally free group actions and from the orbits of flows without fixed points.\nThey are a basic object of differential topology and dynamics, because individual leaves can be dense or wind around in complicated ways.\n\n## Explanations\n\n### L1 human\n\nThink of the pages of a book, or the layers of an onion without its centre.\nNear any point the space looks like a stack of parallel sheets, but globally a single sheet can wander through the whole space.\nOn a torus, take all lines of a fixed slope.\nIf the slope is rational, each line closes into a circle; if it is irrational, each line wraps around forever and comes close to every point.\nBoth families are foliations of the torus by curves.\n",
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