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}
}
• Published 8 November 2018
• Mathematics
• arXiv: Geometric Topology
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 $D^{per}_{C^*\times C… Expand Dualizable link homology • Mathematics • 2019 We modify our previous construction of link homology in order to include a natural duality functor$\mathfrak{F}$. To a link$L$we associate a triply-graded module$HXY(L)$over the gradedExpand Soergel bimodules and matrix factorizations. • Mathematics, Physics • 2020 We establish an isomorphism between the Khovanov-Rozansky triply graded link homology and the geometric triply graded homology due to the authors. Hence we provide an interpretation of theExpand On categorical Donaldson-Thomas theory for local surfaces We introduce the notion of$\mathbb{C}^{\ast}$-equivariant categorical Donaldson-Thomas theories for moduli spaces of stable sheaves on the total space of a canonical line bundle on a smoothExpand 3D TQFT and HOMFLYPT homology • Mathematics, Physics • 2018 In this note we propose a 3D TQFT such that its Hilbert space on$S^2$, which intersects with defect surfaces along a (possibly self-intersecting) curve$C$is the HOMFLYPT homology of the link whoseExpand Mirror symmetry and line operators • Physics, Mathematics • 2019 We study half-BPS line operators in 3d N $$\mathcal{N}$$ = 4 gauge theories, focusing in particular on the algebras of local operators at their junctions. It is known that there are two basic typesExpand Notes on Matrix Factorizations and Knot Homology These are the notes of the lectures delivered by the author at CIME in June 2018. The main purpose of the notes is to provide an overview of the techniques used in the construction of the triplyExpand Cyclotomic expansions of HOMFLY-PT colored by rectangular Young diagrams • Mathematics, Physics • 2019 We conjecture a closed-form expression of HOMFLY-PT invariants of double twist knots colored by rectangular Young diagrams where the twist is encoded in interpolation Macdonald polynomials. We alsoExpand On window theorem for categorical Donaldson-Thomas theories on local surfaces and its applications In this paper, we prove a window theorem for categorical Donaldson-Thomas theories on local surfaces as an analogue of window theorem for GIT quotient stacks. We give two applications of our mainExpand #### References SHOWING 1-10 OF 41 REFERENCES Knot homology and sheaves on the Hilbert scheme of points on the plane • Mathematics • 2016 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 • Mathematics • 2017 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 • Mathematics • 2017 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. • 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 theExpand Equivariant Matrix Factorizations and Hamiltonian reduction • Mathematics • 2015 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 • Mathematics • 2016 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
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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
• Mathematics
• 2018
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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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