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  "body": "\n## Summary\n\nIn 3-manifold topology, a handlebody of genus $g$ is the compact orientable $3$-manifold obtained from a $3$-ball by attaching $g$ one-handles.\nIt is a solid version of the closed orientable surface of [[genus|NJ787GZS1N]] $g$, which is its boundary.\nIt is a ball for $g = 0$, a solid torus for $g = 1$, and a solid double torus for $g = 2$.\nEvery closed orientable $3$-manifold is obtained by gluing two handlebodies of the same genus along their boundaries, which is a [[Heegaard splitting|EDE9919B5R]].\nMore generally, the word handlebody is also used for any manifold with a given [[handle decomposition|9V11N8VVTP]].\n\n## Explanations\n\n### L1 human\n\nA handlebody is the solid inside of a surface with holes, like a solid doughnut or a solid pretzel.\nTake a ball of clay and attach $g$ solid handles to it, like the handle of a cup; the result is a handlebody of genus $g$.\nA solid doughnut is the handlebody of genus $1$, and its surface is the torus.\nA thickened version of any connected graph drawn in space is also a handlebody.\n",
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