منابع مشابه
Odd 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...
متن کاملOn Khovanov Homology
This paper will start from basic knot theory to define the Jones polynomial, then define and explore Khovanov homology, with computations. Two main goals are to present a proposition about the knot mirror and to explore the Khovanov homology of some classes of knots. Elementary algebra will be the only necessary prerequisite for this paper, though familiarity with basic homology will be useful....
متن کاملA computation in Khovanov-Rozansky Homology
We investigate the Khovanov-Rozansky invariant of a certain tangle and its compositions. Surprisingly the complexes we encounter reduce to ones that are very simple. Furthermore, we discuss a “local” algorithm for computing Khovanov-Rozansky homology and compare our results with those for the “foam” version of sl3-homology.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2016
ISSN: 0001-8708
DOI: 10.1016/j.aim.2016.02.007