Open AccessNoncommutative solenoids and the Gromov-Hausdorff propinquity
Author(s) -
Frédéric Latrémolière,
Judith Packer
Publication year - 2016
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/13229
Subject(s) - noncommutative geometry , mathematics , hausdorff space , pure mathematics , noncommutative quantum field theory , solenoid , space (punctuation) , metric space , noncommutative algebraic geometry , quantum , mathematical analysis , quantum mechanics , physics , linguistics , philosophy
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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