The Podles spheres converge to the sphere

We prove that the Podles spheres \(S_q^2\) converge in quantum Gromov-Hausdorff distance to the classical 2-sphere as the deformation parameter \(q\) tends to 1. Moreover, we construct a \(q\)-deformed analogue of the fuzzy spheres, and prove that they converge to \(S_q^2\) as their linear dimension...

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Bibliographic Details
Published in:arXiv.org 2022-03
Main Authors: Aguilar, Konrad, Kaad, Jens, Kyed, David
Format: Article
Language:English
Subjects:
Convergence
Deformation
Metric space
Spheres
Online Access:Get full text
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Summary:We prove that the Podles spheres \(S_q^2\) converge in quantum Gromov-Hausdorff distance to the classical 2-sphere as the deformation parameter \(q\) tends to 1. Moreover, we construct a \(q\)-deformed analogue of the fuzzy spheres, and prove that they converge to \(S_q^2\) as their linear dimension tends to infinity, thus providing a quantum counterpart to a classical result of Rieffel.
ISSN:2331-8422
DOI:10.48550/arxiv.2102.12761