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On Khovanov's categorification of the Jones polynomial

Dror Bar-Natan

Algebraic & Geometric Topology 2 (2002) 337–370

DOI: 10.2140/agt.2002.2.337

arXiv: math.QA/0201043

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.

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Keywords

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

Mathematical Subject Classification

Primary: 57M25

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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