THE NON-COMMUTATIVE METRIC GEOMETRY OF QUANTUM SU(2)

Rieffel's theory of compact quantum metric spaces provides an elegant non-commutative extension of the classical theory of compact metric spaces that is well aligned with Connes' non-commutative geometry. Recently, the quantum metric structure of q-deformed spaces has begun to unravel. In my talk, I will describe how Woronowicz's quantum SU(2) can be endowed with a natural Dirac operator which, in turn, provides it with a compact quantum metric structure. Moreover, I will explain how the resulting family of compact quantum metric spaces can be shown to vary continuously in the deformation parameter q with respect to Rieffel's quantum Gromov-Hausdorff distance. The talk is based on joint work with Jens Kaad as well as earlier joint works with Konrad Aguilar, Thomas Gotfredsen and Jens Kaad.