Legendrian links and the spanning tree model for Khovanov homology
نویسندگان
چکیده
The Khovanov homology has led to many interesting new developments in knot theory and related fields. See Lee [4, 5], Ng [6], Plamenevskaya [7] and Rasmussen [8] for examples. It is still very difficult to compute the Khovanov homology in general. Recently, A Champanerkar and I Kofman [2] and, independently, S Wehrli [11] constructed a spanning tree model for the Khovanov homology based on the spanning tree expansion of the Jones polynomial introduced by M Thistlethwaite in [10]. Though the spanning tree model does not completely determine the Khovanov homology, it does greatly simplify the Khovanov chain complex used to compute the Khovanov homology. In some cases, such simplifications are enough to deduce interesting results. For example, Lee’s result on the Khovanov homology of alternating knots is reproved in [2, 11] by the spanning tree model.
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