Noncommutative Solenoids and the Gromov-Hausdorff Propinquity
Noncommutative metric geometry, Gromov-Hausdorff convergence, Monge-Kantorovich distance, quantum metric spaces, Lip-norms
We prove that noncommutative solenoids are limits, in the sense of the Gromov-Hausdorff propinquity, of quantum tori. From this observation, we prove that noncommutative solenoids can be approximated by finite dimensional quantum compact metric spaces and that they form a continuous family of quantum compact metric spaces over the space of multipliers of the solenoid, properly metrized.
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Frédéric Latrémolière, and Judith Packer. “Noncommutative Solenoids and the Gromov-Hausdorff Propinquity.” Proceedings of the American Mathematical Society, vol. 145, no. 5, 2017, pp. 2043–2057. doi: 10.1090/proc/13229.