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  "body": "\n## Summary\n\nA Dehn twist is a self-homeomorphism of a [[surface|VGJJVBZ1MQ]].\nIt cuts the surface along a simple closed curve, twists one side by a full turn, and glues back.\nIt is the identity outside a thin annulus around the curve.\nDehn twists are the basic elements of the [[mapping class group|JV5NYG913V]] of a surface: by the [[Dehn–Lickorish theorem|BG3EH18KRE]] finitely many of them generate it.\n\n## Explanations\n\n### L1 human\n\nTake a garden hose, hold one end fixed, and turn the other end once around.\nThe hose itself is twisted in a narrow band, and away from that band nothing moves.\nOn a surface, do the same in a thin band around a loop.\nA straight line crossing the band gets wrapped once around the loop.\nOn a torus, a twist around the meridian turns the longitude into a curve that goes once around each way.\n",
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