English

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.

Keywords

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

R2 v1 2026-06-22T04:14:59.226Z