The Podles spheres converge to the sphere

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.

34 pages

References in corpus (4)

• Spectral truncations in noncommutative geometry and operator systems
• Dynamical Systems on Spectral Metric Spaces
• C*-algebraic quantum Gromov-Hausdorff distance
• A residue formula for the fundamental Hochschild 3-cocycle for SUq(2)

Cited by in corpus (1)

• Convergence of Fourier truncations for compact quantum groups and finitely generated groups