Pure Braid Group Presentations via Longest Elements
Group Theory
2023-04-03 v3 Algebraic Geometry
Abstract
This paper gives a new, simplified presentation of the classical pure braid group. The generators are given by the squares of the longest elements over connected subgraphs, and we prove that the only relations are either commutators or certain palindromic length 5 box relations. This presentation is motivated by twist functors in algebraic geometry, but the proof is entirely Coxeter-theoretic. We also prove that the analogous set does not generate for all Coxeter arrangements, which in particular answers a question of Donovan and Wemyss.
Cite
@article{arxiv.2208.02120,
title = {Pure Braid Group Presentations via Longest Elements},
author = {Caroline Namanya},
journal= {arXiv preprint arXiv:2208.02120},
year = {2023}
}
Comments
Final version, to appear in Journal of Algebra