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Leafwise smoothing laminations. (English) Zbl 0978.57011
Summary: 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 D. Gabai in [AMS/IP Stud. Adv. Math. 2 (pt. 2), 1-33 (1997; Zbl 0888.57025)]. Consequently, any such lamination admits the structure of a Riemann surface lamination, and therefore useful structure theorems of A. Candel [Ann. Sci. Éc. Norm. Supér., IV. Sér. 26, No. 4, 489-516 (1993; Zbl 0785.57009)] and E. Ghys [Dynamique et géométrie complexes, Panoramas et Syntheses 8 (1999; Zbl 1010.00008)] apply.

MSC:
57M50 General geometric structures on low-dimensional manifolds
57N10 Topology of general \(3\)-manifolds (MSC2010)
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References:
[1] A Candel, Uniformization of surface laminations, Ann. Sci. École Norm. Sup. \((4)\) 26 (1993) 489 · Zbl 0785.57009 · numdam:ASENS_1993_4_26_4_489_0 · eudml:82347
[2] D Gabai, Problems in foliations and laminations, AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 1 · Zbl 0888.57025
[3] É Ghys, Laminations par surfaces de Riemann, Panor. Synthèses 8, Soc. Math. France (1999) 49 · Zbl 1018.37028 · smf.emath.fr
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