2013/02/27 by William Jaco, William H. Jaco, J. Hyam Rubinstein +3
Computer Science · Mathematics · #57M99 #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Primary 57N10 #Secondary 57M50 #math.GT #msc:57M50 #msc:57M99 #msc:57N10
paper · pdf · doi:10.48550/arxiv.1302.6921
48 pages, 45 figures
arxiv created 2013/02/27 · openalex publication_date 2013/02/27 · arxiv updated 2013/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.