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

2023/07/10 by Justin Malestein, Malestein, Justin, Andrew Putman +1
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2307.04882

openalex publication_date 2023/07/10 · openalex created_date 2023/07/13 · openalex updated_date 2026/07/28

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.

Related

• On the length of the shortest non-trivial element in the derived and the lower central series
• Word Length Formulae and Normal Forms of Conjugacy Classes in Surface Groups
• A new construction for the shortest non-trivial element in the lower central series
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• Artin groups of type (2,3,n)