Resolving extensions of finitely presented systems

TL;DR

This paper generalizes key results from zero-dimensional systems to higher dimensions, establishing the existence of u-resolving Smale space extensions for finitely presented systems and their properties.

Contribution

It introduces the construction of u-resolving Smale space extensions for finitely presented systems and characterizes their minimal and lifting properties.

Findings

Existence of u-resolving Smale space extensions for finitely presented systems

Minimal u-resolving extensions for transitive systems

Lifting of finite-to-one factor maps through u-resolving maps

Abstract

In this paper we extend certain central results of zero dimensional systems to higher dimensions. The first main result shows that if (Y,f) is a finitely presented system, then there exists a Smale space (X,F) and a u-resolving factor map $\pi_+: X\to Y$. If the finitely presented system is transitive, then we show there is a canonical minimal u-resolving Smale space extension. Additionally, we show that any finite-to-one factor map between transitive finitely presented systems lifts through u-resolving maps to an s-resolving map.