The Burau representations of loop braid groups

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.

15 pages, 11 figures, 1 table. Final version, to appear in Comptes Rendus - Mathématique

References in corpus (2)

• The integral cohomology of the group of loops
• On matrix representations for generalized braid groups

Cited by in corpus (1)

• When the lower central series stops: a comprehensive study for braid groups and their relatives