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

## TL;DR

This paper demonstrates that the fundamental group of real line arrangement complements and the torsion in their lower central series quotients are not solely determined by combinatorial data, using computer-assisted proofs and counterexamples.

## Contribution

It provides the first counterexamples showing that these topological invariants are not determined by intersection lattice data.

## Key findings

- Fundamental groups are not determined by intersection lattices.
- Torsion in lower central series quotients is not combinatorially determined.
- Counterexamples refute previous assumptions in the field.

## 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.