Khovanov homology, open books, and tight contact structures

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dc.creatorBaldwin, John A.
dc.creatorPlamenevskaya, Olga
dc.date2008-08-18
dc.date2008-09-26
dc.date.accessioned2026-07-07T10:05:10Z
dc.date.available2026-07-07T10:05:10Z
dc.descriptionWe define the reduced Khovanov homology of an open book (S,h), and we identify a distinguished "contact element" in this group which may be used to establish the tightness or non-fillability of contact structures compatible with (S,h). 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 previously by the first author.
dc.descriptionAdded Proposition 1.4 regarding non-fillability. Expanded Lemma 5.1 and corrected its proof
dc.identifierhttps://arxiv.org/abs/0808.2336
dc.identifierhttp://arxiv.org/abs/0808.2336
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169931
dc.subjectGeometric Topology
dc.subjectSymplectic Geometry
dc.titleKhovanov homology, open books, and tight contact structures
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