Geodesic
Zeros of the Jones polynomial are dense in the complex plane
The electronic journal of combinatorics, Tome 17 (2010)

Voir la notice de l'article provenant de la source The Electronic Journal of Combinatorics website

Zbl EuDML
In this paper, we present a formula for computing the Tutte polynomial of the signed graph formed from a labeled graph by edge replacements in terms of the chain polynomial of the labeled graph. Then we define a family of 'ring of tangles' links and consider zeros of their Jones polynomials. By applying the formula obtained, Beraha-Kahane-Weiss's theorem and Sokal's lemma, we prove that zeros of Jones polynomials of (pretzel) links are dense in the whole complex plane.
DOI : 10.37236/366
Classification : 05C10, 05C22, 05C31, 57M15, 82B20
Mots-clés : Tutte polynomial of a signed graph 
Xian'an Jin; Fuji Zhang; Fengming Dong; Eng Guan Tay. Zeros of the Jones polynomial are dense in the complex plane. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/366
@article{10_37236_366,
     author = {Xian'an Jin and Fuji Zhang and Fengming Dong and Eng Guan Tay},
     title = {Zeros of the {Jones} polynomial are dense in the complex plane},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/366},
     zbl = {1230.05110},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/366/}
}
TY  - JOUR
AU  - Xian'an Jin
AU  - Fuji Zhang
AU  - Fengming Dong
AU  - Eng Guan Tay
TI  - Zeros of the Jones polynomial are dense in the complex plane
JO  - The electronic journal of combinatorics
PY  - 2010
VL  - 17
UR  - http://geodesic.mathdoc.fr/articles/10.37236/366/
DO  - 10.37236/366
ID  - 10_37236_366
ER  - 
%0 Journal Article
%A Xian'an Jin
%A Fuji Zhang
%A Fengming Dong
%A Eng Guan Tay
%T Zeros of the Jones polynomial are dense in the complex plane
%J The electronic journal of combinatorics
%D 2010
%V 17
%U http://geodesic.mathdoc.fr/articles/10.37236/366/
%R 10.37236/366
%F 10_37236_366

Cité par Sources :