Title: Ordering Garside groups,
Abstract: We introduce a condition on Garside groups that we call Dehornoy structure.
An iteration of such a structure leads to a left order on the group. We show
conditions for a Garside group to admit a Dehornoy structure, and we apply
these criteria to prove that the Artin groups of type A and I 2 (m), m $\ge$ 4,
have Dehornoy structures. We show that the left orders on the Artin groups of
type A obtained from their Dehornoy structures are the Dehornoy orders. In the
case of the Artin groups of type I 2 (m), m $\ge$ 4, we show that the left
orders derived from their Dehornoy structures coincide with the orders obtained
from embeddings of the groups into braid groups. 20F36