Leafwise smoothing laminations

Details Leafwise smoothing laminations Leafwise smoothing laminations

2001-11-09

arxiv.org/abs/math/0111119v1

Algebr. Geom. Topol. 1 (2001) 579-587

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-29.abs.html

Scientific paper

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.

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