The geometry monoid of left self-distributivity

We develop a counterpart to Garsideʹs analysis of the braid monoid Bn+ relevant for the monoid MLD that describes the geometry of the left self-distributivity identity. The monoid MLD extends B∞+, of which it shares many properties, with the exception that it is not a direct limit of finitely generated monoids. By introducing a convenient local version of the fundamental elements Δ, we prove that right least common multiples exist in MLD, and, more generally, that MLD resembles a generalized Artin monoid.