ON COMPLEX LINE ARRANGEMENTS AND THEIR BOUNDARY MANIFOLDS

Vincent Florens (1) , Benoît Guerville-Ballé (1) , Miguel A. Marco Buzunariz (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 ICMAT - Instituto de Ciencias Matemáticas

Let A be a line arrangement in the complex projective plane CP2. We define and describe the inclusion map of the boundary manifold -the boundary of a close regular neighborhood of A- in the exterior of the arrangement. We obtain two explicit descriptions of the map induced on the fundamental groups. These computations provide a new minimal presentation of the fundamental group of the complement, generalizing Randell's presentation.

Keywords: line arrangement; boundary manifold; incidence graph; wiring diagram

Domains: Geometric Topology [math.GT]

Vincent Florens, Benoît Guerville-Ballé, Miguel A. Marco Buzunariz. ON COMPLEX LINE ARRANGEMENTS AND THEIR BOUNDARY MANIFOLDS. 2013. ⟨hal-00825063v2⟩