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



Duke Mathematical Journal
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Knot homology via derived categories of coherent sheaves, I: The $\mathfrak{sl}(2)$-case

Sabin Cautis and Joel Kamnitzer

Source: Duke Math. J. Volume 142, Number 3 (2008), 511-588.

Abstract

Using derived categories of equivariant coherent sheaves, we construct a categorification of the tangle calculus associated to $\mathfrak{sl}(2)$ and its standard representation. Our construction is related to that of Seidel and Smith [SS] by homological mirror symmetry. We show that the resulting doubly graded knot homology agrees with Khovanov homology (see [Kh1])

Primary Subjects: 14F05, 57M27

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1208958387
Digital Object Identifier: doi:10.1215/00127094-2008-012

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