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Knot homology via derived categories of coherent sheaves I, sl(2) case

Sabin Cautis·Joel Kamnitzer
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Abstract

Using derived categories of equivariant coherent sheaves, we construct a categorification of the tangle calculus associated to sl(2) and its standard representation. Our construction is related to that of Seidel-Smith by homological mirror symmetry. We show that the resulting doubly graded knot homology agrees with Khovanov homology.

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Sabin Cautis, Joel Kamnitzer. 2007-10-17. Knot homology via derived categories of coherent sheaves I, sl(2) case. https://arxiv.org/abs/math/0701194

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