English

On Parallel Lines and Free Group

Geometric Topology 2009-05-11 v1 Algebraic Geometry

Abstract

We show that the fundamental group of the complement of an arrangement of complex lines in the complex plane is a free group if and only if the arrangement is a union of parallel lines.

Keywords

Cite

@article{arxiv.0905.1178,
  title  = {On Parallel Lines and Free Group},
  author = {Kwai-Man Fan},
  journal= {arXiv preprint arXiv:0905.1178},
  year   = {2009}
}

Comments

8 pages

R2 v1 2026-06-21T12:59:32.856Z