Fuzzy tori converge to the flat torus Dirac triple via an extension of spectral propinquity to twisted spectral triples with unbounded twists.
Noncommutative Solenoids and the Gromov-Hausdorff Propinquity
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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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2026 1verdicts
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How to approximate the flat spectral triple of a quantum torus by fuzzy tori : a twisted tale
Fuzzy tori converge to the flat torus Dirac triple via an extension of spectral propinquity to twisted spectral triples with unbounded twists.