Noncommutative metric geometry, quantum Gromov-Hausdorff distance, Monge-Kantorovich distance, Quantum Metric Spaces, Lip-norms, compact C*-metric spaces, Leibniz seminorms, Quantum Tori, Finite dimensional approximations
We introduce the quantum Gromov-Hausdorff propinquity, a new distance between quantum compact metric spaces, which extends the GromovHausdorff 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.
Latrémolière, F. (2013). The Quantum Gromov-Hausdorff Propinquity. Mathematics Preprint Series. Retrieved from https://digitalcommons.du.edu/math_preprints/21