Application of braiding sequences IV: link polynomials and geometric invariants
Annales de l'Institut Fourier, Volume 70 (2020) no. 4, pp. 1431-1475.

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.

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.

Received:
Accepted:
Published online:
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
Stoimenow, Alexander 1

1 Deadok Innopolis Daejon 34125 (Korea)
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Stoimenow, Alexander. Application of braiding sequences IV: link polynomials and geometric invariants. Annales de l'Institut Fourier, Volume 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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