Fundamental groups of real arrangements and torsion in the lower central series quotients

Abstract

By using computer assistance, we prove that the fundamental group of the complement of a real complexified line arrangement is not determined by its intersection lattice, providing a counter-example for a problem of Falk and Randell. We also deduce that the torsion of the lower central series quotients is not combinatorially determined, which gives a negative answer to a question of Suciu.

arXiv commentRevised and expanded, typos fixed. 12 pages, 4 figures, an appendix with a code in GAP. To appear in Experimental Mathematics

References in corpus (8)

• On the fundamental group of the complement of a complex hyperplane arrangement
• The Braid Monodromy of Plane Algebraic Curves and Hyperplane Arrangements
• Fundamental groups of line arrangements: Enumerative aspects
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• Topology and combinatorics of real line arrangements
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Cited by in corpus (2)

• Homology, lower central series, and hyperplane arrangements
• On the non-connectivity of moduli spaces of arrangements: the splitting-polygon structure