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arXiv · 2102.12761

The Podles spheres converge to the sphere

Konrad Aguilar·Jens Kaad·David Kyed
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Abstract

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.

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Konrad Aguilar, Jens Kaad, David Kyed. 2021-02-25. The Podles spheres converge to the sphere. https://doi.org/10.1007/s00220-022-04363-4

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