Corpus ID: 155099892

Dualizable link homology

@article{Oblomkov2019DualizableLH,
  title={Dualizable link homology},
  author={Alexei Oblomkov and Lev Rozansky},
  journal={arXiv: General Topology},
  year={2019}
}
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 graded polynomial ring $R(L)=\mathbb{C}[x_1,y_1,\dots,x_\ell,y_\ell]$. The module has an involution $\mathfrak{F}$ that intertwines the Fourier transform on $R(L)$, $\mathfrak{F}(x_i)=y_i$, $\mathfrak{F}(y_i)=x_i$. In the case when $\ell=1$ the module is free over $R(L)$ and specialization to $x=y=0$ matches with… Expand
Soergel bimodules and matrix factorizations.
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 theExpand
A G ] 2 3 A ug 2 02 1 Algebra and geometry of link homology Lecture notes from the IHES 2021 Summer School
3 Khovanov-Rozansky homology: definitions and computations 6 3.1 Soergel bimodules and Rouquier complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2 Khovanov-Rozansky homology . . .Expand

References

SHOWING 1-10 OF 33 REFERENCES
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
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
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
Knot homology and sheaves on the Hilbert scheme of points on the plane
For each braid $$\beta \in \mathfrak {Br}_n$$β∈Brn we construct a 2-periodic complex $$\mathbb {S}_\beta $$Sβ of quasi-coherent $$\mathbb {C}^*\times \mathbb {C}^*$$C∗×C∗-equivariant sheaves on theExpand
AFFINE BRAID GROUP, JM ELEMENTS AND KNOT HOMOLOGY
In this paper we construct a homomorphism of the affine braid group Brnaff$$ {\mathfrak{Br}}_n^{\mathrm{aff}} $$ in the convolution algebra of the equivariant matrix factorizations on the spaceExpand
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
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
Flag Hilbert schemes, colored projectors and Khovanov-Rozansky homology
Author(s): Gorsky, Eugene; Neguţ, Andrei; Rasmussen, Jacob | Abstract: We construct a categorification of the maximal commutative subalgebra of the type $A$ Hecke algebra. Specifically, we propose aExpand
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
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
...
1
2
3
4
...