Geodesic
On Khovanov’s categorification of the Jones polynomial
Bar-Natan, Dror1
1Institute of Mathematics, The Hebrew University, Giv’at-Ram, Jerusalem 91904, Israel
Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 337-370
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

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.

DOI : 10.2140/agt.2002.2.337
Keywords: categorification, Kauffman bracket, Jones polynomial, Khovanov, knot invariants

Bar-Natan, Dror  1

1 Institute of Mathematics, The Hebrew University, Giv’at-Ram, Jerusalem 91904, Israel 
@article{10_2140_agt_2002_2_337,
     author = {Bar-Natan, Dror},
     title = {On {Khovanov{\textquoteright}s} categorification of the {Jones} polynomial},
     journal = {Algebraic and Geometric Topology},
     pages = {337--370},
     year = {2002},
     volume = {2},
     number = {1},
     doi = {10.2140/agt.2002.2.337},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2002.2.337/}
}
TY  - JOUR
AU  - Bar-Natan, Dror
TI  - On Khovanov’s categorification of the Jones polynomial
JO  - Algebraic and Geometric Topology
PY  - 2002
SP  - 337
EP  - 370
VL  - 2
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2002.2.337/
DO  - 10.2140/agt.2002.2.337
ID  - 10_2140_agt_2002_2_337
ER  - 
%0 Journal Article
%A Bar-Natan, Dror
%T On Khovanov’s categorification of the Jones polynomial
%J Algebraic and Geometric Topology
%D 2002
%P 337-370
%V 2
%N 1
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2002.2.337/
%R 10.2140/agt.2002.2.337
%F 10_2140_agt_2002_2_337
Bar-Natan, Dror. On Khovanov’s categorification of the Jones polynomial. Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 337-370. doi: 10.2140/agt.2002.2.337

[1] D Bar-Natan, This paper's website

[2] S Garoufalidis, A conjecture on Khovanov's invariants, University of Warwick preprint (2001)

[3] J Hoste, M Thistlethwaite, Knotscape

[4] L H Kauffman, On knots, Annals of Mathematics Studies 115, Princeton University Press (1987)

[5] M Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359

[6] M Khovanov, A functor-valued invariant of tangles, Algebr. Geom. Topol. 2 (2002) 665

[7] D Rolfsen, Knots and links, Mathematics Lecture Series 7, Publish or Perish (1990)

[8] R Scharein, KnotPlot

[9] A Stoimenow, Polynomials of knots with up to 10 crossings

[10] S Wolfram, The $\mathrm{Mathematica}^{(R)}$ book, Wolfram Media, Champaign, IL (1999)

Cité par Sources :