Corpus ID: 225094156

# 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}
}
• Published 27 October 2020
• Mathematics, Physics
• arXiv: Geometric Topology
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
Positroids, knots, and $q,t$-Catalan numbers.
• Mathematics
• 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--RozanskyExpand
From the Hecke Category to the Unipotent Locus
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 generalizedExpand
Categorical Chern character and braid groups.
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• 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 theExpand

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