Frontiers of sphere recognition in practice
Geometric Topology
2021-11-29 v4 Computational Geometry
Algebraic Topology
Metric Geometry
Abstract
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.
Cite
@article{arxiv.1405.3848,
title = {Frontiers of sphere recognition in practice},
author = {Michael Joswig and Davide Lofano and Frank H. Lutz and Mimi Tsuruga},
journal= {arXiv preprint arXiv:1405.3848},
year = {2021}
}
Comments
27 pages, 4 figures, 8 tables, revised and updated, new Section 3.2 on processing Regina's census of 4-manifolds with up to six pentachora