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

Cautis, Sabin; Kamnitzer, Joel

Duke Math. J., Tome 141 (2008) no. 1, p. 511-588 / Harvested from Project Euclid

Résumé

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])

Publié le : 2008-04-15
Classification: 14F05, 57M27

@article{1208958387,
     author = {Cautis, Sabin and Kamnitzer, Joel},
     title = {Knot homology via derived categories of coherent sheaves, I: The $\mathfrak{sl}(2)$ -case},
     journal = {Duke Math. J.},
     volume = {141},
     number = {1},
     year = {2008},
     pages = { 511-588},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1208958387}
}

Cautis, Sabin; Kamnitzer, Joel. Knot homology via derived categories of coherent sheaves, I: The $\mathfrak{sl}(2)$ -case. Duke Math. J., Tome 141 (2008) no. 1, pp.  511-588. http://gdmltest.u-ga.fr/item/1208958387/