Bijections of geodesic lamination space preserving left Hausdorff convergence

On a stratification of the space of (projective) measured laminations

“…In Section 4, we shall prove the main result of this paper, namely, the group of self-homeomorphisms of PML that preserve the stratification PS is induced by MCG e . This rigidity result for the action of the (extended) mapping class group is in the lineage of previous results proved by various authors, such as [5,19,13,1] and most recently [15] and [16]. This list being not all-inclusive, we refer to the survey [20].…”