On turbulent relations

TL;DR

This paper extends Hjorth's turbulence theory to non-Polish action equivalence relations, applying it to analyze complex geometric relations like quasi-isometry and Gromov-Hausdorff distance in metric space classification.

Contribution

It generalizes turbulence theory to broader classes of equivalence relations and applies it to the Gromov space, advancing understanding of metric space classification.

Findings

Turbulence theory extended beyond Polish actions.

Analysis of quasi-isometry relation in Gromov space.

Insights into Gromov-Hausdorff distance relation.

Abstract

This paper extends the theory of turbulence of Hjorth to certain classes of equivalence relations that cannot be induced by Polish actions. It applies this theory to analyze the quasi-isometry relation and finite Gromov-Hausdorff distance relation in the space of isometry classes of pointed proper metric spaces, called the Gromov space.