(Conjectural) triply graded link homology groups of the Hopf link and Hilbert schemes of points on the plane

(Conjectural) triply graded link homology groups of the Hopf link and Hilbert schemes of points on the plane

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Hiraku Nakajima, Kyoto University and IAS
Fine Hall 314

Gukov et al. suggested triply graded link homology groups via refined BPS counting on the deformed conifold. Through large N duality they identify their Poincaré polynomials as refined topological vertices. I further apply the geometric engineering to interpret them as holomorphic Euler characteristics of natural vector bundles over Hilbert schemes of points on the affine plane. Then they perfectly make sense mathematically. This work is very preliminary, but I hope it could be developed further.