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Mikhail Khovanov
Mikhail Khovanov, in the late 1990s, will develop a knot invariant that is a categorification of the Jones polynomial.
Khovanov homology allows the knot to become to become a physical object in four spacetime dimensions. This would be instead of being the path of a point particle in 3 dimensions. That being said, it involves ideas closer to real particle physics, as it describes our four dimensional world.
Cumrun Vafa and others have worked to develop a quantum interpretation of Khovanov homology. This was based on earlier work by Vafa with Hirosi Ooguri.
Edward Witten has worked to relate Khovanov homology to theories in 4, 5 or 6 dimensions.
Khovanov homology is like the Jones polynomial, in that once it was discovered, it could be computed by an explicit set of rules. The rules of Khovanov homology are more sophisticated than that of the Jones polynomial.
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