منابع مشابه
Spanning Trees and Khovanov Homology
The Jones polynomial can be expressed in terms of spanning trees of the graph obtained by checkerboard coloring a knot diagram. We show there exists a complex generated by these spanning trees whose homology is the reduced Khovanov homology. The spanning trees provide a filtration on the reduced Khovanov complex and a spectral sequence that converges to its homology. For alternating links, all ...
متن کاملLegendrian links and the spanning tree model for Khovanov homology
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 ...
متن کاملOdd Khovanov Homology
We describe an invariant of links in S which is closely related to Khovanov’s Jones polynomial homology. Our construction replaces the symmetric algebra appearing in Khovanov’s definition with an exterior algebra. The two invariants have the same reduction modulo 2, but differ over Q. There is a reduced version which is a link invariant whose graded Euler characteristic is the normalized Jones ...
متن کاملFast Khovanov Homology Computations
We introduce a local algorithm for Khovanov Homology computations — that is, we explain how it is possible to “cancel” terms in the Khovanov complex associated with a (“local”) tangle, hence canceling the many associated “global” terms in one swoosh early on. This leads to a dramatic improvement in computational efficiency. Thus our program can rapidly compute certain Khovanov homology groups t...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2009
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-09-09729-9