Constructing Complicated Spheres
Combinatorics
2013-03-05 v2 Algebraic Topology
Geometric Topology
Abstract
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.
Cite
@article{arxiv.1302.6856,
title = {Constructing Complicated Spheres},
author = {Mimi Tsuruga and Frank H. Lutz},
journal= {arXiv preprint arXiv:1302.6856},
year = {2013}
}
Comments
4 pages, 6 figures, extended abstract, EuroCG 2013, reference added