# Hilbert schemes and $y$-ification of Khovanov-Rozansky homology

@article{Gorsky2017HilbertSA, title={Hilbert schemes and \$y\$-ification of Khovanov-Rozansky homology}, author={Eugene Gorsky and Matthew Hogancamp}, journal={arXiv: Geometric Topology}, year={2017} }

Author(s): Gorsky, Eugene; Hogancamp, Matthew | Abstract: We define a deformation of the triply graded Khovanov-Rozansky homology of a link $L$ depending on a choice of parameters $y_c$ for each component of $L$, which satisfies link-splitting properties similar to the Batson-Seed invariant. Keeping the $y_c$ as formal variables yields a link homology valued in triply graded modules over $\mathbb{Q}[x_c,y_c]_{c\in \pi_0(L)}$. We conjecture that this invariant restores the missing $Q… Expand

#### 18 Citations

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Unramified affine Springer fibers and isospectral Hilbert schemes

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These are the notes of the lectures delivered by the author at CIME in June 2018. The main purpose of the notes is to provide an overview of the techniques used in the construction of the triply… Expand

A G ] 2 3 A ug 2 02 1 Algebra and geometry of link homology Lecture notes from the IHES 2021 Summer School

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3 Khovanov-Rozansky homology: definitions and computations 6 3.1 Soergel bimodules and Rouquier complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2 Khovanov-Rozansky homology . . .… Expand

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