Inflations of ideal triangulations
Abstract
Starting with an ideal triangulation of 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 triangulations 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 the 3-sphere, 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 nonorientable compact 3-manifold with Klein bottle boundary. Several applications of inflations are discussed.
Keywords
Cite
@article{arxiv.1302.6921,
title = {Inflations of ideal triangulations},
author = {William H. Jaco and J. Hyam Rubinstein},
journal= {arXiv preprint arXiv:1302.6921},
year = {2013}
}
Comments
48 pages, 45 figures