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Noncommutative solenoids and the Gromov-Hausdorff propinquity


Authors: Frédéric Latrémolière and Judith Packer
Journal: Proc. Amer. Math. Soc. 145 (2017), 2043-2057
MSC (2010): Primary 46L89, 46L30, 58B34
DOI: https://doi.org/10.1090/proc/13229
Published electronically: January 31, 2017
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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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Additional Information

Frédéric Latrémolière
Affiliation: Department of Mathematics, University of Denver, Denver, Colorado 80208
Email: frederic@math.du.edu

Judith Packer
Affiliation: Department of Mathematics, University of Colorado, Boulder, Colorado 80309
Email: packer@euclid.colorado.edu

DOI: https://doi.org/10.1090/proc/13229
Keywords: Noncommutative metric geometry, Gromov-Hausdorff convergence, Monge-Kantorovich distance, quantum metric spaces, Lip-norms
Received by editor(s): January 11, 2016
Received by editor(s) in revised form: March 9, 2016, and April 3, 2016
Published electronically: January 31, 2017
Additional Notes: This work was partially supported by a grant from the Simons Foundation (#316981 to the second author)
Communicated by: Yargbese Mathai
Article copyright: © Copyright 2017 American Mathematical Society