arXiv subjects
Publications and source records attributed to Mimi Tsuruga.
Sphere recognition is known to be undecidable in dimensions five and beyond, and no polynomial time method is known in dimensions three and four. Here we report on positive and negative computational results with the goal to explore the limits of sphere recognition from a practical point of view. An important ingredient are randomly constructed discrete Morse functions.
Fast and efficient homology algorithms are in demand in the applied sciences for analyzing solid materials and proteins, processing digital imaging data, or pattern classification among others. Recent advances employ discrete Morse theory as a preprocessor. Research in this area has lead to the need to find complicated test examples. We present an infinite series of examples that have been constructed to test some of the latest algorithms under development. This family of 4-spheres (known as the Akbulut-Kirby spheres) is based on a handlebody construction via finitely presented groups.