Corpus ID: 119641158

Categorical Chern character and braid groups.

@article{Oblomkov2018CategoricalCC,
  title={Categorical Chern character and braid groups.},
  author={Alexei Oblomkov and Lev Rozansky},
  journal={arXiv: Geometric Topology},
  year={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 homology of $S_\beta$. The construction of $S_\beta$ relies on the Chern functor $CH: MF_n^{st}\to D^{per}_{C^*\times C^*}(Hilb_n(C^2))$ defined in the paper together with its adjoint functor $HC$. The properties of these functors lead us to a conjecture that $HC$ sends $D^{per}_{C^*\times C… Expand
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References

SHOWING 1-10 OF 41 REFERENCES
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
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
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
Equivariant Matrix Factorizations and Hamiltonian reduction
Let $X$ be a smooth scheme with an action of an algebraic group $G$. We establish an equivalence of two categories related to the corresponding moment map $\mu : T^*X \to Lie(G)^*$ - the derivedExpand
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
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
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
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
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
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