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  "body": "\n## Summary\n\nA Heegaard splitting cuts a closed orientable [[3-manifold|R20TB2KEQQ]] along a closed surface into two [[handlebodies|AP1KY4EHMA]] of the same genus.\nEvery closed orientable $3$-manifold has one, so each such manifold is described by a surface and a gluing map between the boundaries of two handlebodies.\nThe smallest possible genus is the Heegaard genus, an invariant of the manifold.\n\n## Explanations\n\n### L1 human\n\nA handlebody is a solid ball with some solid handles attached, like the inside of a pretzel.\nTake two such solids with the same number of handles and glue their surfaces together.\nThe result is a closed $3$-dimensional space, and every closed orientable one arises in this way.\nFor example, the $3$-sphere is two solid balls glued along their boundary spheres, and also two solid doughnuts glued along their boundary tori.\n",
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