Algebraic and Geometric Topology 1 (2001), paper no. 29, pages 579-585.

Leafwise smoothing laminations

Danny Calegari

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.

Keywords. Lamination, foliation, leafwise smooth, 3--manifold

AMS subject classification. Primary: 57M50.

DOI: 10.2140/agt.2001.1.579

E-print: arXiv:math.GT/0111119

Submitted: 17 May 2001. (Revised: 15 August 2001.) Accepted: 11 October 2001. Published: 18 October 2001.

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Danny Calegari
Department of Mathematics
Harvard
Cambridge, MA 02138
Email: dannyc@math.harvard.edu
URL: www.math.harvard.edu/~dannyc
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