Annular-Efficient Triangulations of 3-manifolds

Details Annular-Efficient Triangulations of 3-manifolds Annular-Efficient Triangulations of 3-manifolds

2011-08-15

arxiv.org/abs/1108.2936v1

Mathematics

Geometric Topology

21 pages, 6 figures

Scientific paper

A triangulation of a compact 3-manifold is annular-efficient if it is 0-efficient and the only normal, incompressible annuli are thin edge-linking. If a compact 3-manifold has an annular-efficient triangulation, then it is irreducible, boundary-irreducible, and an-annular. Conversely, it is shown that for a compact, irreducible, boundary-irreducible, and an-annular 3-manifold, any triangulation can be modified to an annular-efficient triangulation. It follows that for a manifold satisfying this hypothesis, there are only a finite number of boundary slopes for incompressible and boundary-incompressible surfaces of a bounded Euler characteristic.

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