Khovanov Homology, Open Books, and Tight Contact Structures
نویسنده
چکیده
We define the reduced Khovanov homology of an open book (S, φ), and we identify a distinguished “contact element” in this group which may be used to establish the tightness of contact structures compatible with (S, φ). Our construction generalizes the relationship between the reduced Khovanov homology of a link and the Heegaard Floer homology of its branched double cover. As an application, we give combinatorial proofs of tightness for several contact structures which are not Stein-fillable. Lastly, we investigate a comultiplication structure on the reduced Khovanov homology of an open book which parallels the comultiplication on Heegaard Floer homology defined in [5].
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تاریخ انتشار 2008