no. 4
Application of braiding sequences IV: link polynomials and geometric invariants
[Applications de séquences de tressage IV : polynômes d’entrelacs et invariants géométriques]
Stoimenow, Alexander1
1 Deadok Innopolis Daejon 34125 (Korea)
Annales de l'Institut Fourier, Tome 70 (2020) no. 4, pp. 1431-1475.

Nous appliquons le concept de séquences de tressage aux polynômes de skein et de Conway, mais aussi à quelques invariants géométriques des entrelacs positifs. On donne des estimations pour l’indice des tresses et pour des invariants legendriens, en utilisant le degré et des propriétés de croissance des coefficients du polynôme de Conway. Nous énumérons asymptotiquement à une constante près les entrelacs alternants (et quelques autres) de genre donné par leur indice de tresses.

We apply the concept of braiding sequences to the Conway and skein polynomial, and some geometric invariants of positive links. Using degree and coefficient growth properties of the Conway polynomial, estimates of braid index and Legendrian invariants are given. We enumerate alternating (and some other classes of) links of given genus asymptotically up to constants by braid index.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3371
Classification : 57M25, 57M27, 57M50, 05A16, 05C10
Keywords: positive knot, alternating knot, braid index, genus, link polynomial, Legendrian knot, Bennequin inequality, enumeration
Mot clés : noeud positif, noeud alternant, indice de tresses, genre, invariant polynomial d’entrelacs, noeud legendrien, inégalité de Bennequin, énumération des noeuds

Stoimenow, Alexander 1

1 Deadok Innopolis Daejon 34125 (Korea)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Stoimenow, Alexander. Application of braiding sequences IV: link polynomials and geometric invariants. Annales de l'Institut Fourier, Tome 70 (2020) no. 4, pp. 1431-1475. doi : 10.5802/aif.3371. https://aif.centre-mersenne.org/articles/10.5802/aif.3371/

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