On complex line arrangements and their boundary manifolds

TL;DR

This paper studies the boundary manifolds of complex line arrangements in CP2, providing explicit descriptions of the inclusion map and a new minimal presentation of the fundamental group of the complement.

Contribution

It introduces a novel explicit description of the boundary manifold inclusion map and derives a minimal presentation of the fundamental group for complex line arrangements.

Findings

Explicit descriptions of the boundary manifold inclusion map.

A new minimal presentation of the fundamental group.

Enhanced understanding of the topology of line arrangements.

Abstract

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.