arXiv math/02121112002-12-08math.GT

Boundary curves of surfaces with the 4-plane property

Tao Li

备注：: Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper21.abs.html
发表信息：: Geom. Topol. 6 (2002) 609-647
DOI：: 10.2140/gt.2002.6.609

英文摘要：

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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