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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