Convergence of Cauchy Sequences for the covariant Gromov-Hausdorff propinquity

Abstract

The covariant Gromov-Hausdorff propinquity is a distance on Lipschitz dynamical systems over quantum compact metric spaces, up to equivariant full quantum isometry. It is built from the dual Gromov-Hausdorff propinquity which, as its classical counterpart, is complete. We prove in this paper several sufficient conditions for convergence of Cauchy sequences for the covariant propinquity and apply it to show that many natural classes of dynamical systems are complete for this metric.

arXiv comment24 pages. This version corrects a single typo in Definition 2.23 (post-publication). This paper was the second part of arXiv:1805.11229v1, whose two halves are now in two separated papers: this one and the new version of arXiv:1805.11229