# 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

#### 2 Citations

Soergel bimodules and matrix factorizations.

- Mathematics, Physics
- 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… Expand

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

- 2021

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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