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}
}
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.
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.
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

References

SHOWING 1-10 OF 65 REFERENCES
Khovanov-Rozansky homology and higher Catalan sequences
We give a simple recursion which computes the triply graded Khovanov-Rozansky homology of several infinite families of knots and links, including the $(n,nm\pm 1)$ and $(n,nm)$ torus links forExpand
Hilbert schemes and $y$-ification of Khovanov-Rozansky homology
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 eachExpand
Dualizable link homology
We modify our previous construction of link homology in order to include a natural duality functor $\mathfrak{F}$. To a link $L$ we associate a triply-graded module $HXY(L)$ over the gradedExpand
Geometric representations of graded and rational Cherednik algebras
We provide geometric constructions of modules over the graded Cherednik algebra $\mathfrak{H}^{gr}_\nu$ and the rational Cherednik algebra $\mathfrak{H}^{rat}_\nu$ attached to a simple algebraicExpand
Triply-graded link homology and Hochschild homology of Soergel bimodules
We consider a class of bimodules over polynomial algebras which were originally introduced by Soergel in relation to the Kazhdan–Lusztig theory, and which describe a direct summand of the category ofExpand
Torus knots and the rational DAHA
Author(s): Gorsky, E; Oblomkov, A; Rasmussen, J; Shende, V | Abstract: © 2014. We conjecturally extract the triply graded Khovanov-Rozansky homology of the (m;n) torus knot from the uniqueExpand
The Superpolynomial for Knot Homologies
TLDR
A framework for unifying the sl(N) Khovanov– Rozansky homology with the knot Floer homology is proposed, and a rich formal structure is proposed that is powerful enough to make many nontrivial predictions about the existing knot homologies that can then be checked directly. Expand
Rational Cherednik algebras and Hilbert schemes, II: Representations and sheaves
Let H_c be the rational Cherednik algebra of type A_{n-1} with spherical subalgebra U_c = e H_c e. Then U_c is filtered by order of differential operators with associated graded ring gr U_c =Expand
Flag Hilbert schemes, colored projectors and Khovanov-Rozansky homology
We construct a categorification of the maximal commutative subalgebra of the type A Hecke algebra. Specifically, we propose a monoidal functor from the (symmetric) monoidal category of coherentExpand
The Hilbert scheme of a plane curve singularity and the HOMFLY homology of its link
Author(s): Oblomkov, A; Rasmussen, J; Shende, V; Gorsky, E | Abstract: © 2018, Mathematical Sciences Publishers. All rights reserved. We conjecture an expression for the dimensions of theExpand
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