Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4665668 | Advances in Mathematics | 2014 | 49 Pages |
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 S3S3, 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-orientable compact 3-manifold with Klein bottle boundary. Several applications of inflations are discussed.