Journal article

0-Efficient triangulations of 3-manifolds

W Jaco, JH Rubinstein

JOURNAL OF DIFFERENTIAL GEOMETRY | LEHIGH UNIV | Published : 2003

Abstract

0-efficient triangulations of 3-manifolds are defined and studied. It is shown that any triangulation of a closed, orientable, irreducible 3-manifold M can be modified to a 0-efficient triangulation or M can be shown to be one of the manifolds S3, ℝP3 or L(3, 1). Similarly, any triangulation of a compact, orientable, irreducible, ∂-irreducible 3-manifold can be modified to a 0-efficient triangulation. The notion of a 0-efficient ideal triangulation is defined. It is shown if M is a compact, orientable, irreducible, ∂-irreducible 3-manifold having no essential annuli and distinct from the 3-cell, then Mо admits an ideal triangulation; furthermore, it is shown that any ideal triangulation of s..

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