We show that every topological surface lamination of a 3–manifold M is isotopic to one with smoothly immersed leaves. This carries out a project proposed by Gabai in [Problems in foliations and laminations, AMS/IP Stud. Adv. Math. 2.2 1–33]. Consequently any such lamination admits the structure of a Riemann surface lamination, and therefore useful structure theorems of Candel [Uniformization of surface laminations, Ann. Sci. Ecole Norm. Sup. 26 (1993) 489–516] and Ghys [Dynamique et geometrie complexes, Panoramas et Syntheses 8 (1999)] apply.
"Leafwise smoothing laminations." Algebr. Geom. Topol. 1 (1) 579 - 587, 2001. https://doi.org/10.2140/agt.2001.1.579