We prove that the Podles spheres S2p converge in quantum Gromov-Hausdorff distance to the classical 2-sphere as the deformation parameter p 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.
|Journal||Communications in Mathematical Physics|
|Number of pages||33|
|Publication status||Accepted/In press - 2022|
- 58B32, 58B34, 46L89, 46L30, 81R15, 81R60