Fundamental Groups of Real Arrangements and Torsion in the Lower Central Series Quotients

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

Essential coordinate components of characteristic varieties

In this note we give an algebraic and topological interpretation of essential coordinate components of characteristic varieties and illustrate their importance with an example.Comment: 15 pages, 4 postscript figures, to appear in Mathematical Proceedings of the Cambridge Philosophical Societ