An invariant of tangle cobordisms via subquotients of arc rings

By Yanfeng Chen, Mikhail Khovanov. 2006

75 citations recorded by the source corpus.

We construct an explicit categorification of the action of tangles on tensor powers of the fundamental representation of quantum sl(2).

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7c526be7303053ebe07bea1074d955f3cf3d98d5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Ben Webster
2. Aaron D. Lauda
3. Sabin Cautis
4. C. Stroppel
5. David E. V. Rose
6. Jonathan Brundan
7. Hoel Queffelec
8. Joel Kamnitzer

In Mathematical Physics

1. Aaron D. Lauda
2. Sabin Cautis
3. Ben Webster
4. David E. V. Rose
5. Jonathan Brundan
6. Hoel Queffelec
7. C. Stroppel
8. Joel Kamnitzer

Citations in the corpus

• Highest weight categories arising from Khovanov's diagram algebra II: Koszulity (2008, background): “ This article is the first of a series of four articles studying some slight generalisations Hn m of Khovanov’s diagram algebra, and their quasi-hereditary covers Kn m which were introduced already in [CK], [S]. All of these are positively graded finite dimensional algebras; since Hn m ∼=Hm n and Kmn ”
• 2-block Springer fibers: convolution algebras and coherent sheaves (2008, methodology): “For the general 2-Jordan-block case (not necessarily equally sized), we establish an isomorphism to the more general version of the arc algebra as introduced in [Str09] and [CK06].”
• Quantum link homology via trace functor I (2016, methodology): “shadow on the homotopy bicategory of Chen-Khovanov bimodules, induced by the quantum Hochschild homology. For this purpose, let us examine the homology of tangles constructed by Chen and Khovanov. In [CK14] they defined a family of diagrammatic algebras An, commonly called arc algebras, associated a ”
• Knot homology via derived categories of coherent sheaves II, $\mathfrak{sl}_{m}$ case (2007, methodology): “as the derived category of a graded version of the direct sum of various parabolic category Ofor various Lie algebras glm. Another categorification was constructed by Khovanov in [Kh2] and extended in [CK]. In this categorification Dnwas the derived category of a graded modules over a certain combinat”
• Annular Khovanov homology and knotted Schur–Weyl representations (2015, background): “1The construction of this functor-valued tangle invariant is made more explicit in [11] than in [8], whose focus is on a relationship between the algebras An and category O.”