# Khovanov's homology for tangles and cobordisms

```@article{BarNatan2004KhovanovsHF,
title={Khovanov's homology for tangles and cobordisms},
author={Dror Bar-Natan},
journal={Geometry \& Topology},
year={2004},
volume={9},
pages={1443-1499}
}```
• D. Bar-Natan
• Published 22 October 2004
• Mathematics
• Geometry & Topology
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 pictures a little longer than in other articles on the subject, the required extension becomes essentially tautological. And then a simple application of an appropriate functor (a "TQFT") to our pictures takes them to the familiar realm of complexes of (graded) vector spaces and ordinary homological…
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