# Sutured annular Khovanov-Rozansky homology

@article{Queffelec2015SuturedAK, title={Sutured annular Khovanov-Rozansky homology}, author={Hoel Queffelec and David E. V. Rose}, journal={arXiv: Quantum Algebra}, year={2015} }

We introduce an sl(n) homology theory for knots and links in the thickened annulus. To do so, we first give a fresh perspective on sutured annular Khovanov homology, showing that its definition follows naturally from trace decategorifications of enhanced sl(2) foams and categorified quantum gl(m), via classical skew Howe duality. This framework then extends to give our annular sl(n) link homology theory, which we call sutured annular Khovanov-Rozansky homology. We show that the sl(n) sutured…

## 28 Citations

Evaluations of annular Khovanov-Rozansky homology

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Author(s): Gorsky, Eugene; Wedrich, Paul | Abstract: We describe the universal target of annular Khovanov-Rozansky link homology functors as the homotopy category of a free symmetric monoidal…

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We define a variant of Khovanov homology for links in thickened disks with multiple punctures. This theory is distinct from the one previously defined by Asaeda, Przytycki, and Sikora, but is related…

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We use categorical annular evaluation to give a uniform construction of both $\mathfrak{sl}_n$ and HOMFLYPT Khovanov-Rozansky link homology, as well as annular versions of these theories. Variations…

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For every oriented surface of finite type, we construct a functorial Khovanov homology for links in a thickening of the surface, which takes values in a categorification of the corresponding gl(2)…

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We use Khovanov-Rozansky gl(N) link homology to define invariants of oriented smooth 4-manifolds, as skein modules constructed from certain 4-categories with well-behaved duals. The technical heart…

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Annular Khovanov homology and knotted Schur–Weyl representations

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Let $\mathbb{L}\subset A\times I$ be a link in a thickened annulus. We show that its sutured annular Khovanov homology carries an action of $\mathfrak{sl}_{2}(\wedge )$ , the exterior current algebra…

Extremal weight projectors II.

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In previous work, we have constructed diagrammatic idempotents in an affine extension of the Temperley-Lieb category, which describe extremal weight projectors for sl(2), and which categorify…

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