The Quantum Gromov-Hausdorff Propinquity
Abstract
We introduce the quantum Gromov-Hausdorff propinquity, a new distance between quantum compact metric spaces, which extends the Gromov-Hausdorff distance to noncommutative geometry and strengthens Rieffel's quantum Gromov-Hausdorff distance and Rieffel's proximity by making *-isomorphism a necessary condition for distance zero, while being well adapted to Leibniz seminorms. This work offers a natural solution to the long-standing problem of finding a framework for the development of a theory of Leibniz Lip-norms over C*-algebras.
Cite
@article{arxiv.1302.4058,
title = {The Quantum Gromov-Hausdorff Propinquity},
author = {Frederic Latremoliere},
journal= {arXiv preprint arXiv:1302.4058},
year = {2015}
}
Comments
49 Pages. This is the first half of 1302.4058v2, which has been accepted in Trans. Amer. Math. Soc. The second half is now a different paper entitled "Convergence of Fuzzy Tori and Quantum Tori for the quantum Gromov-Hausdorff Propinquity: an explicit approach"