A generalized Desargues configuration and the pure braid group

✍ Scribed by Raul Cordovil; António Guedes de Oliveira; Michel Las Vergnas

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 459 KB
• Volume: 160
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(95)00152-m

✦ Synopsis

In this paper, a configuration with n = (g) points in the plane is described. This configuration, as a matroid, is a Desargues configuration if d = 5, and the union of (~) such configurations if d > 5. As an oriented matroid, it is a rank 3 truncation of the directed complete graph on d vertices. From this fact, it follows from a version of the Lefschetz Zariski theorem implied by results of Salvetti that the fundamental group ~ of the complexification of its line arrangement is Artin's pure (or coloured) braid group on d strands.

In this paper we obtain, by using techniques introduced by Salvetti, a new algorithm for finding a presentation of ~ based on this particular configuration.