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  "body": "\n## Summary\n\nA Morse–Bott function is a smooth function whose critical points form submanifolds, and which is nondegenerate in the directions normal to these submanifolds.\nIt generalizes a [[Morse function|KPQ96640ZJ]], whose critical submanifolds are points.\nRaoul Bott introduced the notion for functions with symmetry, whose critical points come in families.\nAn example is the energy on spaces of paths in a symmetric space.\n\n## Explanations\n\n### L1 human\n\nThink of a ring-shaped doughnut lying flat on a table, and take the height as the function.\nThe lowest points form a whole circle, and so do the highest points, so the critical points are not isolated.\nStill, in the direction across each circle the height curves up or down in a clean way.\nSuch a function is Morse–Bott: degenerate only along its critical circles and nondegenerate across them.\nA simpler example is $f(x, y) = x^2$ on the plane, whose critical points form the line $x = 0$.\n",
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