Boundary curves of surfaces with the 4-plane property

Details Boundary curves of surfaces with the 4-plane property Boundary curves of surfaces with the 4-plane property

2002-12-08

arxiv.org/abs/math/0212111v1

Geom. Topol. 6 (2002) 609-647

Mathematics

Geometric Topology

Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper21.abs.html

Scientific paper

Let M be an orientable and irreducible 3-manifold whose boundary is an incompressible torus. Suppose that M does not contain any closed nonperipheral embedded incompressible surfaces. We will show in this paper that the immersed surfaces in M with the 4-plane property can realize only finitely many boundary slopes. Moreover, we will show that only finitely many Dehn fillings of M can yield 3-manifolds with nonpositive cubings. This gives the first examples of hyperbolic 3-manifolds that cannot admit any nonpositive cubings.

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