A Garside type structure on the combed mapping class group

I begin by a pictorial introduction to Garside graphs
which I hope is appealing. A Garside graph is a combinatorial
version of (a convex subset of) a real vector space. The oldest
and best known example of a Garside graph is a certain Cayley
graph of the braid group.

The combed mapping class group is a rather big subgroup of a
surface mapping class group, namely, consisting of those elements
preserving a nowhere vanishing vector field up to homotopy.

I construct a Garside graph on which the combed mapping class
group acts faithfully. It uses geodesic laminations on hyperbolic
surfaces which I shall recall.