Journal article

Inflations of ideal triangulations

William Jaco, J Hyam Rubinstein

ADVANCES IN MATHEMATICS | ACADEMIC PRESS INC ELSEVIER SCIENCE | Published : 2014

Abstract

Starting with an ideal triangulation of M°, the interior of a compact 3-manifold M with boundary, no component of which is a 2-sphere, we provide a construction, called an inflation of the ideal triangulation, to obtain a strongly related triangulation of M itself. Besides a step-by-step algorithm for such a construction, we provide examples of an inflation of the two-tetrahedra ideal triangulation of the complement of the figure-eight knot in S3, giving a minimal triangulation, having ten tetrahedra, of the figure-eight knot exterior. As another example, we provide an inflation of the one-tetrahedron Gieseking manifold giving a minimal triangulation, having seven tetrahedra, of a non-orient..

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Grants

Awarded by NSF/DMS


Awarded by Australian Research Council


Funding Acknowledgements

[ "The first author was partially supported by NSF/DMS Grants (DMS-9971719 and DMS-0204707), The Grayce B. Kerr Foundation, The American Institute of Mathematics (AIM), and The Visiting Research Scholar Program at University of Melbourne (Australia).", "The second author was partially supported by The Australian Research Council (DP0664296) and The Grayce B. Kerr Foundation." ]