Word length versus lower central series depth for surface groups and RAAGs

TL;DR

This paper establishes lower bounds on the minimal word length needed to represent nontrivial elements in the lower central series of surface groups and RAAGs, advancing understanding of their algebraic structure.

Contribution

It provides new lower bounds for word lengths in the lower central series of surface groups and RAAGs, a novel result in algebraic group theory.

Findings

Lower bounds on word length for surface groups

Lower bounds on word length for RAAGs

Enhanced understanding of lower central series structure

Abstract

For surface groups and right-angled Artin groups, we prove lower bounds on the shortest word in the generators representing a nontrivial element of the kth term of the lower central series.