Résume | Garside groups are generalisations of the well-known Artin braid groups. Basically, the class of Garside groups captures the fundamental algebraic properties of braid groups and separates them from properties arising from a specific geometrical or topological context. The most fundamental characteristics is the existence of the greedy normal form. I will start by recalling the greedy normal form for braids and by explaining how this idea is abstractly formulated in the Garside group setting. We will then look at some invariants of conjugacy classes which were introduced to solve certain computational problems in Garside groups. In the second part of the talk, we will see that the theoretical properties of these established invariants are in some sense unsatisfactory. This will lead us to the definition of what appears to be a more natural theoretical structure. The presented results are joint work with Juan Gonzalez-Meneses. |