Noncommutative solenoids and the Gromov-Hausdorff propinquity

Latrémolière, Frédéric; Packer, Judith

doi:10.1090/proc/13229

Noncommutative solenoids and the Gromov-Hausdorff propinquity
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Proc. Amer. Math. Soc. 145 (2017), 2043-2057 Request permission

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.

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