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.

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

References in corpus (2)

• An arithmetic Zariski 4-tuple of twelve lines
• An arithmetic Zariski pair of line arrangements with non-isomorphic fundamental group

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