Minimum ideal triangulations of hyperbolic 3-manifolds

Abstract

Let σ(n) be the minimum number of ideal hyperbolic tetrahedra necessary to construct a finite volume n-cusped hyperbolic 3-manifold, orientable or not. Let σor(n) be the corresponding number when we restrict ourselves to orientable manifolds. The correct values of σ(n) and σor(n) and the corresponding manifolds are given for n=1,2,3,4 and 5. We then show that 2 n-1≤σ(n)≤σor(n)≤4 n-4 for n≥5 and that σor(n)≥2 n for all n. © 1991 Springer-Verlag New York Inc.