Constructing Complicated Spheres
Mimi Tsuruga, Frank H. Lutz

TL;DR
This paper introduces an infinite series of complex 4-sphere examples, called Akbulut-Kirby spheres, designed to test advanced homology algorithms used in analyzing solid materials, proteins, and digital data.
Contribution
It provides a new family of complicated 4-sphere test cases constructed through handlebody methods based on finitely presented groups.
Findings
The Akbulut-Kirby spheres serve as challenging benchmarks for homology algorithms.
They demonstrate the need for robust algorithms capable of handling complex topological structures.
The construction method links group theory with topological sphere examples.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsTopological and Geometric Data Analysis · Digital Image Processing Techniques · Geometric and Algebraic Topology
