Geodesic
Leafwise smoothing laminations
Calegari, Danny1
1Department of Mathematics, Harvard, Cambridge MA 02138, USA
Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 579-587
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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.

DOI : 10.2140/agt.2001.1.579
Keywords: lamination, foliation, leafwise smooth, 3–manifold

Calegari, Danny  1

1 Department of Mathematics, Harvard, Cambridge MA 02138, USA 
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Calegari, Danny. Leafwise smoothing laminations. Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 579-587. doi: 10.2140/agt.2001.1.579

[1] A Candel, Uniformization of surface laminations, Ann. Sci. École Norm. Sup. $(4)$ 26 (1993) 489

[2] D Gabai, Problems in foliations and laminations, from: "Geometric topology (Athens, GA, 1993)", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 1

[3] É Ghys, Laminations par surfaces de Riemann, from: "Dynamique et géométrie complexes (Lyon, 1997)", Panor. Synthèses 8, Soc. Math. France (1999) 49

[4] R C Kirby, L C Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulations, Princeton University Press (1977)

[5] E E Moise, Geometric topology in dimensions 2 and 3, Graduate Texts in Mathematics 47, Springer (1977)

[6] Y Rudyak, Piecewise linear structures on topological manifolds,

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