On Parallel Lines and Free Group

2009/05/08 by Kwai-Man Fan, Fan, Kwai-Man
Mathematics · #14H30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #math.AG #math.GT #msc:14H30

paper · pdf · doi:10.48550/arxiv.0905.1178

8 pages

arxiv created 2009/05/08 · arxiv updated 2009/12/01

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.

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