Khovanov's homology for tangles and cobordisms
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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 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 invariants.
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Forward citations
Cited by 2 Pith papers
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Categorification of some Penrose polynomials
Constructs doubly- and triply-graded Penrose-type homologies for ribbon graphs via TQFT cube of resolutions whose Euler characteristics recover Penrose polynomial specializations.
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Khovanov complexes for bipartite links
Shows that the Kauffman-Khovanov 2²-hypercube reduces to the bipartite 3-hypercube for N=2, confirming consistency of the reduction for bipartite links.
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