On Khovanov’s categorification of the Jones polynomial

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.

Additional material

Keywords

categorification, Kauffman bracket, Jones polynomial, Khovanov, knot invariants

Mathematical Subject Classification 2000

Primary: 57M25

References

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Publication

Received: 13 January 2002

Accepted: 27 February 2002

Published: 21 May 2002

Authors

Dror Bar-Natan
Institute of Mathematics The Hebrew University Giv’at-Ram Jerusalem 91904 Israel
http://www.ma.huji.ac.il/~drorbn

Volume 2, issue 1 (2002)

Dror Bar-Natan

Abstract