In the context of metric geometry, we introduce a new necessary and sufficient condition for
the convergence of an inductive sequence of quantum compact metric spaces for the …

We generalize the Fejér-Riesz operator systems defined for the circle group by Connes and
van Suijlekom to the setting of compact matrix quantum groups and their ergodic actions on …

We prove that the Podleś 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 aq …

We define a metric on the class of metric spectral triples, which is null exactly between
unitarily equivalent spectral triples. This metric dominates the propinquity, and thus implies …

The spectral propinquity is a distance, up to unitary equivalence, on the class of metric
spectral triples. We prove in this paper that if a sequence of metric spectral triples converges …

In this paper, we present a characterization of compact quantum metric spaces in terms of
finite dimensional approximations. This characterization naturally leads to the introduction of …

We introduce a two parameter family of Dirac operators on quantum SU (2) and analyse
their properties from the point of view of non-commutative metric geometry. It is shown that …

We prove that there is a unique Levi-Civita connection on the one-forms of the Dabrowski-
Sitarz spectral triple for the Podle\'{s} sphere $ S^{2} _ {q} $. We compute the full curvature …

We show how to equip the crossed product between a group of polynomial growth and a
compact quantum metric space with a compact quantum metric space structure. When the …

We introduce in this paper the dual modular propinquity, a complete metric, up to full
modular quantum isometry, on the class of metrized quantum vector bundles, ie of Hilbert …