Absence of barriers in dynamical triangulation

TL;DR

This paper investigates whether unrecognizable manifolds in dynamical triangulation lead to unreachable states, finding no evidence of such barriers in the case of the 5-sphere.

Contribution

It provides a numerical analysis of unrecognizable manifolds, specifically the 5-sphere, showing that potential barriers do not manifest in practice.

Findings

No signs of unreachable states in $S^5$ triangulations

Unrecognizability does not necessarily imply barriers in dynamical triangulation

Supports the reliability of dynamical triangulation methods for certain unrecognizable manifolds

Abstract

Due to the unrecognizability of certain manifolds there must exist pairs of triangulations of these manifolds that can only be reached from each other by going through an intermediate state that is very large. This might reduce the reliability of dynamical triangulation, because there will be states that will not be reached in practice. We investigate this problem numerically for the manifold $S^5$, which is known to be unrecognizable, but see no sign of these unreachable states.