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

2007/01/06 by Cautis, Sabin, Kamnitzer, Joel
#Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.math/0701194

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.

Related

• Knot homology via derived categories of coherent sheaves IV, coloured links
• Khovanov homology and the symmetry group of a knot
• Lectures on knot homology
• An sl(2) tangle homology and seamed cobordisms
• Knot invariants arising from homological operations on Khovanov homology