Laminar Branched Surfaces in 3-manifolds

Details Laminar Branched Surfaces in 3-manifolds Laminar Branched Surfaces in 3-manifolds

2002-03-31

arxiv.org/abs/math/0204012v1

Geom. Topol. 6(2002) 153-194

Mathematics

Geometric Topology

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper6.abs.html

Scientific paper

We define a laminar branched surface to be a branched surface satisfying the following conditions: (1) Its horizontal boundary is incompressible; (2) there is no monogon; (3) there is no Reeb component; (4) there is no sink disk (after eliminating trivial bubbles in the branched surface). The first three conditions are standard in the theory of branched surfaces, and a sink disk is a disk branch of the branched surface with all branch directions of its boundary arcs pointing inwards. We will show in this paper that every laminar branched surface carries an essential lamination, and any essential lamination that is not a lamination by planes is carried by a laminar branched surface. This implies that a 3-manifold contains an essential lamination if and only if it contains a laminar branched surface.

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