A Compactness Theorem for The Dual Gromov-Hausdorff Propinquity
Abstract
We prove a compactness theorem for the dual Gromov-Hausdorff propinquity as a noncommutative analogue of the Gromov compactness theorem for the Gromov-Hausdorff distance. Our theorem is valid for subclasses of quasi-Leibniz compact quantum metric spaces of the closure of finite dimensional quasi-Leibniz compact quantum metric spaces for the dual propinquity. While finding characterizations of this class proves delicate, we show that all nuclear, quasi-diagonal quasi-Leibniz compact quantum metric spaces are limits of finite dimensional quasi-Leibniz compact quantum metric spaces. This result involves a mild extension of the definition of the dual propinquity to quasi-Leibniz compact quantum metric spaces, which is presented in the first part of this paper.
Keywords
Cite
@article{arxiv.1501.06121,
title = {A Compactness Theorem for The Dual Gromov-Hausdorff Propinquity},
author = {Frederic Latremoliere},
journal= {arXiv preprint arXiv:1501.06121},
year = {2018}
}
Comments
40 Pages. Version 4 includes several minor corrections and is accepted in the Indiana University Mathematics Journal