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Robert Lipshitz : The Jones polynomial as Euler characteristic

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We will start by defining the Jones polynomial of a knot, and discussing some of its applications. We will then explain a refinement of the Jones polynomial, called Khovanov homology, and give some applications of this refinement. We will conclude by discussing a further refinement, called a Khovanov homotopy type; this part is joint work with Sucharit Sarkar.

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