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  "body": "\n## Summary\n\nTransversality is the condition that two [[submanifolds|VKFW27WXEZ]], or a smooth map and a submanifold, meet in general position.\nAt each meeting point their tangent spaces together span the tangent space of the ambient manifold.\nTransverse intersections are again submanifolds, of the expected dimension, and they persist under small perturbations.\nTransversality is the basic notion of general position in differential topology and underlies intersection numbers, degree theory and cobordism.\n\n## Explanations\n\n### L1 human\n\nTwo lines in the plane that cross at an angle meet transversally, while two lines that touch along a common direction do not.\nA small wiggle cannot destroy a transverse crossing, but it can easily separate two curves that only touch.\nIn space, a plane and a line meet transversally when the line pierces the plane rather than lying in it.\nTwo curves in $\\R^3$ meet transversally only if they do not meet at all, because two lines cannot span three dimensions.\n",
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