The Podleś Spheres Converge to the Sphere

Konrad Aguilar, Jens Kaad*, David Kyed

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Abstrakt

We prove that the Podleś spheres S2q 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 S2q as their linear dimension tends to infinity, thus providing a quantum counterpart to a classical result of Rieffel.

OriginalsprogEngelsk
TidsskriftCommunications in Mathematical Physics
Vol/bind392
Udgave nummer3
Sider (fra-til)1029-1061
ISSN0010-3616
DOI
StatusUdgivet - jun. 2022

Bibliografisk note

Funding Information:
The authors gratefully acknowledge the financial support from the Independent Research Fund Denmark through Grant Nos. 9040-00107B and 7014-00145B. Furthermore, they would like to thank Marc Rieffel for pointing out the reference [], and the anonymous referees for their careful reading of the manuscript.

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