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Leafwise smoothing laminations

Danny Calegari

Algebraic & Geometric Topology 1 (2001) 579–587

arXiv: math.GT/0111119

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
Mathematical Subject Classification 2000
Primary: 57M50
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Publication
Received: 17 May 2001
Revised: 15 August 2001
Accepted: 11 October 2001
Published: 18 October 2001
Authors
Danny Calegari
Department of Mathematics
Harvard
Cambridge MA 02138
USA
www.math.harvard.edu/~dannyc