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  "body": "\n## Summary\n\nAn immersion is a smooth map between [[smooth manifolds|F45VQ47GPV]] whose [[differential|6P9PXQDSEN]] is injective at every point.\nLocally it looks like the inclusion of $\\R^m$ into $\\R^n$, but globally it may cross itself.\nImmersions are the maps along which a manifold can be drawn in another one without corners or folds.\nTheir classification up to regular homotopy is a model case of the homotopy principle.\n\n## Explanations\n\n### L1 human\n\nThink of drawing a curve on paper with a pen that never stops moving.\nThe drawing may cross itself, but it never has a corner or a point where the pen stands still.\nThat is an immersion of a curve into the plane.\nFor example, the figure eight $t \\mapsto (\\sin 2t, \\sin t)$ immerses the circle into $\\R^2$: its velocity is never zero, but the image crosses itself at the origin.\nAn immersion that is one-to-one and a homeomorphism onto its image is called an embedding.\n",
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