# An invariant of tangle cobordisms

@article{Khovanov2002AnIO, title={An invariant of tangle cobordisms}, author={Mikhail Khovanov}, journal={Transactions of the American Mathematical Society}, year={2002}, volume={358}, pages={315-327} }

We construct a new invariant of tangle cobordisms. The invariant of a tangle is a complex of bimodules over certain rings, well-defined up to chain homotopy equivalence. The invariant of a tangle cobordism is a homomorphism between complexes of bimodules assigned to boundaries of the' cobordism.

## 14 Citations

An invariant of tangle cobordisms via subquotients of arc rings

- Mathematics
- 2006

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

A Burau-Alexander 2-functor on tangles

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We construct a weak 2-functor from the bicategory of oriented tangles to a bicategory of Lagrangian cospans. This functor simultaneously extends the Burau representation of the braid groups, its…

Functoriality of Khovanov homology

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In this paper we prove that every Khovanov homology associated to a Frobenius algebra of rank $2$ can be modified in such a way as to produce a TQFT on oriented links, that is a monoidal functor from…

Khovanov's homology for tangles and cobordisms

- Mathematics
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We give a fresh introduction to the Khovanov Homology theory for knots and links, with special emphasis on its extension to tangles, cobordisms and 2-knots. By staying within a world of topological…

A Lie theoretic categorification of the coloured Jones polynomial

- MathematicsJournal of Pure and Applied Algebra
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An oriented model for Khovanov homology

- Mathematics
- 2010

We give an alternative presentation of Khovanov homology of links with strict functoriality result over integers. The construction uses an oriented $sl(2)$ state model allowing a natural definition…

An sl(2) tangle homology and seamed cobordisms

- Mathematics
- 2007

We construct a bigraded (co)homology theory which depends on a parameter a, and whose graded Euler characteristic is the quantum sl(2) link invariant. We follow Bar-Natan's approach to tangles on one…

On the functoriality of sl(2) tangle homology.

- Mathematics
- 2019

We construct an explicit equivalence between the (bi)category of gl(2) webs and foams and the Bar-Natan (bi)category of Temperley-Lieb diagrams and cobordisms. With this equivalence we can fix…

sl(2) tangle homology with a parameter and singular cobordisms

- Mathematics
- 2008

We construct a bigraded cohomology theory which depends on one parameter a, and whose graded Euler characteristic is the quantum sl.2/ link invariant. We follow Bar-Natan’s approach to tangles on one…

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