Title

Noncommutative Solenoids and the Gromov-Hausdorff Propinquity

Document Type

Article

Publication Date

1-31-2017

Keywords

Noncommutative metric geometry, Gromov-Hausdorff convergence, Monge-Kantorovich distance, quantum metric spaces, Lip-norms

Organizational Units

College of Natual Science and Mathematics, Mathematics

Abstract

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.

Publication Statement

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