A generalized Desargues configuration and the pure braid group

• Type: Article in International Scientific Journal
• Date: 1996

Authors

Cordovil, R (Author) Other; deOliveira, AG (Author) FCUP; LasVergnas, M (Author) Other

Journal

Title: Discrete Mathematics

Vol. 160

Pages: 105-113

ISSN: 0012-365X

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-001-DCS

DOI: 10.1016/0012-365x(95)00152-m

Abstract (EN): In this paper, a configuration with n = ((d)(2)) points in the plane is described. This configuration, as a matroid, is a Desargues configuration if d = 5, and the union of ((d)(5)) 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 pi of the complexification of its line arrangement is Artin's pure (or coloured) braid group on n strands. In this paper we obtain, by using techniques introduced by Salvetti, a new algorithm for finding a presentation of pi based on this particular configuration.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 9