Quantum Metric Spaces and the Gromov-Hausdorff Propinquity
Abstract
We present a survey of the dual Gromov-Hausdorff propinquity, a noncommutative analogue of the Gromov-Hausdorff distance which we introduced to provide a framework for the study of the noncommutative metric properties of C*-algebras. We first review the notions of quantum locally compact metric spaces, and present various examples of such structures. We then explain the construction of the dual Gromov-Hausdorff propinquity, first in the context of quasi-Leibniz quantum compact metric spaces, and then in the context of pointed quantum proper metric spaces. We include a few new result concerning perturbations of the metrics on Leibniz quantum compact metric spaces in relation with the dual Gromov-Hausdorff propinquity.
Keywords
Cite
@article{arxiv.1506.04341,
title = {Quantum Metric Spaces and the Gromov-Hausdorff Propinquity},
author = {Frederic Latremoliere},
journal= {arXiv preprint arXiv:1506.04341},
year = {2021}
}
Comments
89 Pages. This paper is a survey, except section 3.7 which includes new results. Material included from arXiv:1501.06121, arXiv:1406.0233, arXiv:1404.6330, arXiv:1311.0104, arXiv:1312.0069, arXiv:1302.4058, arXiv:1208.2398, arXiv:math/0510320, arXiv:math/0310241