Knot homology via derived categories of coherent sheaves II, $\mathfrak{sl}_{m}$ case
By Sabin Cautis, Joel Kamnitzer. 2007
95 citations recorded by the source corpus.
Using derived categories of equivariant coherent sheaves we construct a knot homology theory which categorifies the quantum $\mathfrak{sl}_{m}$ knot polynomial. Our knot homology naturally satisfies the categorified MOY relations and is conjecturally isomorphic to Khovanov–Rozansky homology. Our construction is motivated by the geometric Satake correspondence and is related to Manolescu’s by homological mirror symmetry.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/544d46e5809630b866db09f5f09be5a6b0a605c8
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In Geometry and Topology
- Sabin Cautis
- Pavel Putrov
- Joel Kamnitzer
- Sergei Gukov
- Anthony M. Licata
- David E. V. Rose
- C. Vafa
- E. Witten
In Mathematical Physics
- Sabin Cautis
- Joel Kamnitzer
- E. Witten
- Sergei Gukov
- Pavel Putrov
- Anthony M. Licata
- David E. V. Rose
- C. Vafa
Citations in the corpus
- COHERENT SHEAVES AND CATEGORICAL sl2 ACTIONS (2009, background): “Also there is a functor from the derived category of coherent sheaves on T (G(k;N)) to dg modules over H (G(k;N)) by taking Ext(OG(k;N); ), because Ext (OG(k;N);OG(k;N)) = H (G(k;N)) (see Remark 5.11 in [ CK1 ]).”
- BPS spectra and 3-manifold invariants (2017, background): “For example, in addition to its original combinatorial definition [12], the Khovanov homology of knots by now has definitions based on matrix factorizations [13], algebraic geometry [37], symplectic geometry [38–40], etc.”
- Derived equivalences for cotangent bundles of Grassmannians via categorical 𝔰𝔩2 actions (2009, unknown): “(ii) If Hom(Ai+k+2[k],Ai) = 0 for all i � 0,k � 1, then (A� ,f� ) has a convolution. Proof. See Proposition 8.3 of [ CK1 ].”
- A link-splitting spectral sequence in Khovanov homology (2013, background): “Cautis and Kamnitzer have given a description of Khovanov homology in terms of derived categories of coherent sheaves [5], which is mirror to symplectic Khovanov homology.”