Khovanov homology for virtual links using cobordisms

Details Khovanov homology for virtual links using cobordisms Khovanov homology for virtual links using cobordisms

2011-11-02

arxiv.org/abs/1111.0609v2

Mathematics

Geometric Topology

50 pages, Lots of figures; typos and minor mistakes corrected, new examples added

Scientific paper

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.

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