5 papers
How to approximate the flat spectral triple of a quantum torus by fuzzy tori : a twisted tale
Frederic Latremoliere
We prove that the classical and the quantum flat torus can be rigorously approximated at a differential level by finite-dimensional fuzzy tori within the framework of the spectral…
Spectral continuity of almost commutative manifolds for the topology on Riemannian metrics
Frederic Latremoliere
Almost commutative models provide a framework for Connes' work on the standard model of particle physics. These models are constructed as products of a the canonical spectral tripl…
The quantum Gromov-Hausdorff Hypertopology on the class of pointed Proper Quantum Metric Spaces
Frederic Latremoliere
We introduce a hypertopology, induced by an inframetric up to full quantum isometry, on the class of pointed proper quantum metric spaces, which are separable, possibly non-unital,…
Collapse in Noncommutative Geometry and Spectral Continuity
Carla Farsi, Frederic Latremoliere
If two compact quantum metric spaces are close in the metric sense, then how similar are they, as noncommutative spaces? In the classical realm of Riemannian geometry, informally,…
Continuity for the spectral propinquity of the Dirac operators associated with an analytic path of Riemannian metrics
Carla Farsi, Frederic Latremoliere
We prove that a polynomial path of Riemannian metrics on a closed spin manifold induces a continuous field in the spectral propinquity of metric spectral triples.