Leafwise smoothing laminations

Danny Calegari

doi:10.2140/agt.2001.1.579

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Home > Journals > Algebr. Geom. Topol. > Volume 1 > Issue 1 > Article

2001 Leafwise smoothing laminations

Danny Calegari

Algebr. Geom. Topol. 1(1): 579-587 (2001). DOI: 10.2140/agt.2001.1.579

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Abstract

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.