Knot homology via derived categories of coherent sheaves I, sl(2) case
By Sabin Cautis, Joel Kamnitzer. 2007
128 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/360fb0e7442dc6eecb0932ca529469fcd64f6da2
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In Computational Theory and Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- A categorification of quantum sl(n) (2008, unknown): “In most or all of these examples, see [3, 7, 10, 31, 33], the weight decomposition of representations lifts to a direct sum decomposition of categories, so one obtains a categorification of the idempotent 1λ as the functor of projection onto the corresponding direct summand (the only possible except”
- New derived symmetries of some hyperkähler varieties (2011, background): “Cautis and Kamnitzer [9] considered a similar example and enriched the structure in a different direction, getting representations of sl2 and of other Lie algebras in later papers.”
- Fivebranes and Knots (2011, methodology): “In one construction [21,22], the effective theory on Σ seems to be a Landau-Ginzburg B-model (so that the branes are matrix factorizations); in a second construction [23], the effective theory is a B-model with target space a certain Kahler manifold; other approaches [24, 25] are based on A-models.”