Braids in Pau – An Introduction

Artal Bartolo, Enrique; Florens, Vincent

doi:10.5802/ambp.292

Braids in Pau – An Introduction
[Tresses à Pau – une introduction]

Artal Bartolo, Enrique ¹ ; Florens, Vincent ²

¹ Departamento de Matemáticas, IUMA, Facultad de Ciencias, Universidad de Zaragoza, c/ Pedro Cerbuna, 12, 50009 Zaragoza, Spain
² Laboratoire de Mathématiques et de leurs Applications - PAU UMR CNRS 5142 Bâtiment IPRA - Université de Pau et des Pays de l’Adour Avenue de l’Université - BP 1155 64013 PAU CEDEX, France

Annales mathématiques Blaise Pascal, Tome 18 (2011) no. 1, pp. 1-14.

Résumé
Abstract

Dans ce travail, nous décrivons les liaisons historiques entre l’étude de variétés de dimension $3$ (notamment, la théorie de nœuds) et l’étude de la topologie des courbes planes complexes, dont l’accent est posé sur le rôle des groupes de tresses et des invariantes du type Alexander (torsions, différents incarnations des polynômes d’Alexander). Nous finissons en présentant un example avec des calculs détaillés.

In this work, we describe the historic links between the study of $3$ -dimensional manifolds (specially knot theory) and the study of the topology of complex plane curves with a particular attention to the role of braid groups and Alexander-like invariants (torsions, different instances of Alexander polynomials). We finish with detailed computations in an example.

MR Zbl

DOI : 10.5802/ambp.292

Classification : 14H50, 14D05, 57M25, 57C10, 20F36
Keywords: Knots, curves, braid groups, torsion, Alexander polynomial
Mot clés : Nœuds, courbes, torsion, polynômes d’Alexander

Affiliations des auteurs :

Artal Bartolo, Enrique ¹ ; Florens, Vincent ²

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Artal Bartolo, Enrique; Florens, Vincent. Braids in Pau – An Introduction. Annales mathématiques Blaise Pascal, Tome 18 (2011) no. 1, pp. 1-14. doi : 10.5802/ambp.292. http://www.numdam.org/articles/10.5802/ambp.292/

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