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

Enrique Artal Bartolo; Benoît Guerville-Ballé; Juan Viu-Sos

doi:10.1080/10586458.2018.1428131

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arXiv · 1704.04152

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

Enrique Artal Bartolo·Benoît Guerville-Ballé·Juan Viu-Sos

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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.

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Enrique Artal Bartolo, Benoît Guerville-Ballé, Juan Viu-Sos. 2018-01-11. Fundamental groups of real arrangements and torsion in the lower central series quotients. https://doi.org/10.1080/10586458.2018.1428131

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