# Soergel bimodules and matrix factorizations.

@article{Oblomkov2020SoergelBA, title={Soergel bimodules and matrix factorizations.}, author={Alexei Oblomkov and Lev Rozansky}, journal={arXiv: Geometric Topology}, year={2020} }

We establish an isomorphism between the Khovanov-Rozansky triply graded link homology and the geometric triply graded homology due to the authors. Hence we provide an interpretation of the Khovanov-Rozansky homology of the closure of a braid $\beta$ as the space of derived sections of a $\mathbb{C}^*\times \mathbb{C}^*$- equivariant sheaf $Tr(\beta)$ on the Hilbert scheme $Hilb_n(\mathbb{C}^2)$, thus proving a version of Gorsky-Negut-Rasmussen conjecture \cite{GorskyNegutRasmussen16}. As a… Expand

#### 3 Citations

Positroids, knots, and $q,t$-Catalan numbers.

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- 2020

We relate the mixed Hodge structure on the cohomology of open positroid varieties (in particular, their Betti numbers over $\mathbb{C}$ and point counts over $\mathbb{F}_q$) to Khovanov--Rozansky… Expand

From the Hecke Category to the Unipotent Locus

- Mathematics
- 2021

Let W be the Weyl group of a split semisimple group G. Its Hecke category HW can be built from pure perverse sheaves on the double flag variety of G. By developing a formalism of generalized… Expand

Categorical Chern character and braid groups.

- Mathematics
- 2018

To a braid $\beta\in Br_n$ we associate a complex of sheaves $S_\beta$ on $Hilb_n(C^2)$ such that the previously defined triply graded link homology of the closure $L(\beta)$ is isomorphic to the… Expand

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