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.

arXiv comment15 pages, 11 figures, 1 table. Final version, to appear in Comptes Rendus - Mathématique

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Cited by in corpus (2)

• Topological representations of motion groups and mapping class groups -- a unified functorial construction
• When the lower central series stops: a comprehensive study for braid groups and their relatives