The Burau representations of loop braid groups
Geometric Topology
2023-03-07 v2 Algebraic Topology
Abstract
We give a simple topological construction of the Burau representations of the loop braid groups. There are four versions: defined either on the non-extended or extended loop braid groups, and in each case there is an unreduced and a reduced version. Three are not surprising, and one could easily guess the correct matrices to assign to generators. The fourth is more subtle, and does not seem combinatorially obvious, although it is topologically very natural.
Cite
@article{arxiv.2109.11468,
title = {The Burau representations of loop braid groups},
author = {Martin Palmer and Arthur Soulié},
journal= {arXiv preprint arXiv:2109.11468},
year = {2023}
}
Comments
15 pages, 11 figures, 1 table. Final version, to appear in Comptes Rendus - Math\'ematique