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On Khovanov’s categorification of the Jones polynomial. (English) Zbl 0998.57016
This paper contributes a lot to understand Khovanov’s work on the categorification of the Jones polynomial [M. Khovanov, Duke Math. J. 101, No. 3, 359-426 (2000; Zbl 0960.57005); A functor-valued invariant of tangles, Archiv. Math. QA/0103190)]. Furthermore, the author provides some computations of the Khovanov polynomial $$Kh(L)$$ of a link projection $$L$$, including one that shows that Khovanov’s invariant is strictly stronger than the Jones polynomial. Finally, a table of the values of Khovanov’s polynomial for all prime knots with up to 11 crossings completes the paper.

##### MSC:
 57M25 Knots and links in the $$3$$-sphere (MSC2010) 57M27 Invariants of knots and $$3$$-manifolds (MSC2010)
##### Keywords:
Kauffman bracket; knot invariants; Khovanov polynomial
##### Software:
KnotPlot; Knotscape; Mathematica
Full Text:
##### References:
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