English

The Podles spheres converge to the sphere

Operator Algebras 2022-04-20 v3 Functional Analysis

Abstract

We prove that the Podles spheres Sq2S_q^2 converge in quantum Gromov-Hausdorff distance to the classical 2-sphere as the deformation parameter qq tends to 1. Moreover, we construct a qq-deformed analogue of the fuzzy spheres, and prove that they converge to Sq2S_q^2 as their linear dimension tends to infinity, thus providing a quantum counterpart to a classical result of Rieffel.

Keywords

Cite

@article{arxiv.2102.12761,
  title  = {The Podles spheres converge to the sphere},
  author = {Konrad Aguilar and Jens Kaad and David Kyed},
  journal= {arXiv preprint arXiv:2102.12761},
  year   = {2022}
}

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34 pages