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  "body": "\n## Summary\n\nThe curve complex of a [[surface|VGJJVBZ1MQ]] is a [[simplicial complex|V8GZ0W1ZZ5]].\nIts vertices are the isotopy classes of essential simple closed curves, and its simplices are sets of curves that can be made pairwise disjoint.\nThe [[mapping class group|JV5NYG913V]] acts on it by simplicial automorphisms.\nHarvey introduced it, and Masur and Minsky proved that it is hyperbolic in the sense of Gromov.\nIt is a central tool in the study of mapping class groups and of Teichmüller space.\n\n## Explanations\n\n### L1 human\n\nDraw all the essentially different loops on a surface, one dot for each.\nJoin two dots by an edge when the two loops can be drawn without crossing.\nFill in a triangle when three loops can be drawn pairwise without crossing, and so on.\nThe resulting shape is infinite and tangled, but it records how all loops on the surface sit with respect to each other.\n",
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