Computational Ergodicity of $s^4$

TL;DR

This paper investigates the computational properties of four-manifolds, focusing on the ergodicity of triangulations, and finds no evidence of algorithmic barriers in the case of the 4-sphere.

Contribution

It demonstrates that, unlike some four-manifolds, the triangulations of the 4-sphere do not exhibit large algorithmic barriers, suggesting different computational complexity characteristics.

Findings

No observed barriers for triangulations of S^4

Differences in algorithmic recognizability among four-manifolds

Insights into the ergodic behavior of 4-manifold triangulations

Abstract

It is known that there are four-manifolds which are not algorithmically recognizable. This implies that there exist triangulations of these manifolds which are separated by large barriers from the point of view of the computer algorithm. We have not observed these barriers for triangulations of $S^4$.