Noncommutative Solenoids and the Gromov-Hausdorff Propinquity

Publication Date

1-31-2017

Document Type

Article

Organizational Units

Mathematics

Keywords

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

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

Copyright held by author or publisher. User is responsible for all copyright compliance.

This document is currently not available here.

Share

COinS