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  "body": "\n## Summary\n\nThe genus of a closed orientable [[surface|VGJJVBZ1MQ]] is its number of handles.\nIt is the largest number of disjoint simple closed curves along which the surface can be cut without falling apart.\nBy the [[classification of surfaces|2SFM73YET0]], the genus determines a closed orientable surface up to homeomorphism, and it is related to the [[Euler characteristic|RNDDWDAFJ5]] by $\\chi = 2 - 2g$.\nThe same number appears as the genus of an algebraic curve and of a compact Riemann surface.\n\n## Explanations\n\n### L1 human\n\nThe genus counts holes in the sense of a doughnut, not of a cup.\nA sphere has genus $0$, a doughnut has genus $1$, and a pretzel with two holes has genus $2$.\nOn a doughnut you can cut along one circle around the tube and still have one piece, a cylinder.\nAny second disjoint cut then splits it, so the genus is $1$.\n",
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