A Note on Words in Braid Monoids

The purpose of this note is to give a self-contained (apart from simple facts about Coxeter groups) and we hope a bit shorter and more understandable account of some results of [[C1], [C2]] on normal forms of braids which are themselves based on the papers [ [D1], [T]]. In particular a motivation was to give a proof of Proposition 5.1 that we use in [ [B-M]]. Some proofs and results from Section 2 onwards seem to be new. I thank several people for improvements from earlier versions of the manuscript: M. Geck for pointing out some errors, F. Digne for pointing out that some results donʹt need the braid group to be of finite type, and J.-Y. Hée for suggesting (and providing) further improvements in that direction.