Virtual Khovanov homology using cobordisms

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  • Daniel Tubbenhauer
    Daniel TubbenhauerDenmark
We give a geometric interpretation of the Khovanov complex for virtual links. Geometric interpretation means that we use a cobordism structure like D. Bar-Natan, but we allow non orientable cobordisms. Like D. Bar-Natans geometric complex our construction should work for virtual tangles too. This geometric complex allows, in contrast to the geometric version of V. Turaev and P. Turner, a direct extension of the classical Khovanov complex (h=t=0) and of the variant of Lee (h=0,t=1). Furthermore we give a classification of all unoriented TQFTs which can be used to define virtual link homologies with this geometric construction.
Original languageEnglish
Article number1450046
JournalJournal of Knot Theory and Its Ramifications
Volume23
Issue number9
Number of pages91
ISSN0218-2165
DOIs
StatePublished - 7 Oct 2014

    Keywords

  • Diagrammatic categorication, Virtual knots, Knot homologies

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