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  "body": "\n## Summary\n\nKhovanov homology is an invariant of oriented [[links|1A5WRCNTM3]] that takes values in bigraded abelian groups.\nMikhail Khovanov built it from a cube of smoothings of a diagram, as a categorification of the [[Jones polynomial|4SPC17FPXE]].\nIts graded Euler characteristic is the Jones polynomial, but it carries strictly more information.\nKronheimer and Mrowka proved that it detects the [[unknot|1TQ06R4Q66]].\n\n## Explanations\n\n### L1 human\n\nThe [[Kauffman bracket|JYKVYS4N32]] computes the Jones polynomial by summing over all ways to smooth the crossings of a diagram.\nKhovanov homology replaces each term of that sum by a group and each sign by a map between groups.\nThe result is a chain complex, and its homology does not depend on the diagram.\nCounting dimensions with signs gives back the Jones polynomial.\nThe extra structure lets it tell apart knots that the Jones polynomial cannot.\n",
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