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Proceedings of the American Mathematical Society

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Noncommutative solenoids and the Gromov-Hausdorff propinquity
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by Frédéric Latrémolière and Judith Packer PDF
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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Additional Information
  • Frédéric Latrémolière
  • Affiliation: Department of Mathematics, University of Denver, Denver, Colorado 80208
  • MR Author ID: 760927
  • Email: frederic@math.du.edu
  • Judith Packer
  • Affiliation: Department of Mathematics, University of Colorado, Boulder, Colorado 80309
  • MR Author ID: 135125
  • Email: packer@euclid.colorado.edu
  • 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
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 2043-2057
  • MSC (2010): Primary 46L89, 46L30, 58B34
  • DOI: https://doi.org/10.1090/proc/13229
  • MathSciNet review: 3611319