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  "body": "\n## Summary\n\nA virtual knot is an equivalence class of knot diagrams that may have, besides ordinary crossings, virtual crossings that are not really there.\nLouis Kauffman introduced them as a generalization of classical [[knots|QYEAZTYGPT]].\nGeometrically, virtual knots are knots in thickened surfaces, taken up to a suitable stabilization.\nClassical knots form a part of virtual knot theory: two classical knots that are equivalent as virtual knots are equivalent as classical knots.\n\n## Explanations\n\n### L1 human\n\nSome knot drawings cannot be made without extra crossings that come only from the flat paper.\nA virtual crossing is such a fake crossing, drawn with a small circle around it.\nVirtual knots allow these crossings and treat them as invisible: strands may slide freely across them.\nThey can be pictured as knots drawn on a surface with handles, such as a torus, where the fake crossings disappear.\n",
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