Geometry & Topology, Vol. 6 (2002)
Paper no. 21, pages 609-647.
Boundary curves of surfaces with the 4-plane property
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.
3-manifold, immersed surface, nonpositive cubing, 4-plane property, immersed branched surface.
AMS subject classification.
Secondary: 57M25, 57N10, 57M07.
Submitted to GT on 23 March 2001.
(Revised 15 March 2002.)
Paper accepted 15 November 2002.
Paper published 6 December 2002.
Notes on file formats
Department of Mathematics, Oklahoma State University
Stillwater, OK 74078, USA
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