Algebraic and Geometric Topology 2 (2002), paper no. 16, pages 337-370.

On Khovanov's categorification of the Jones polynomial

Dror Bar-Natan

Abstract. The working mathematician fears complicated words but loves pictures and diagrams. We thus give a no-fancy-anything picture rich glimpse into Khovanov's novel construction of `the categorification of the Jones polynomial'. For the same low cost we also provide some computations, including one that shows that Khovanov's invariant is strictly stronger than the Jones polynomial and including a table of the values of Khovanov's invariant for all prime knots with up to 11 crossings.
The program and associated data files can be downloaded:

Keywords. Categorification, Kauffman bracket, Jones polynomial, Khovanov, knot invariants

AMS subject classification. Primary: 57M25.

DOI: 10.2140/agt.2002.2.337

E-print: arXiv:math.QA/0201043

Submitted: 13 January 2002. Accepted: 27 February 2002. Published: 21 May 2002.

Notes on file formats

Dror Bar-Natan
Institute of Mathematics, The Hebrew University
Giv'at-Ram, Jerusalem 91904, Israel
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