منابع مشابه
Khovanov Homology for Alternating Tangles
We describe a “concentration on the diagonal” condition on the Khovanov complex of tangles, show that this condition is satisfied by the Khovanov complex of the single crossing tangles (!) and ("), and prove that it is preserved by alternating planar algebra compositions. Hence, this condition is satisfied by the Khovanov complex of all alternating tangles. Finally, in the case of 0-tangles, me...
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The purpose of this paper is to interpret polynomial invariants of strongly invertible links in terms of Khovanov homology theory. To a divide, that is a proper generic immersion of a finite number of copies of the unit interval and circles in a 2-disc, one can associate a strongly invertible link in the 3-sphere. This can be generalized to signed divides : divides with + or sign assignment to ...
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: Journal of Knot Theory and Its Ramifications
سال: 2010
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216510007863