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arXiv · 1506.04341

Quantum Metric Spaces and the Gromov-Hausdorff Propinquity

Frederic Latremoliere
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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.

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BibTeXRIS

Frederic Latremoliere. 2015-06-14. Quantum Metric Spaces and the Gromov-Hausdorff Propinquity. https://arxiv.org/abs/1506.04341

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