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Metric Approximations of Spectral Triples on the Sierpiński Gasket and other fractal curves
Therese-Marie Landry, Michel L. Lapidus, Frederic Latremoliere
Noncommutative geometry provides a framework, via the construction of spectral triples, for the study of the geometry of certain classes of fractals. Many fractals are constructed…
Bunce-Deddens algebras as quantum Gromov-Hausorff distance limits of circle algebras
Konrad Aguilar, Frederic Latremoliere, Timothy Rainone
We show that Bunce-Deddens algebras, which are AT-algebras, are also limits of circle algebras for Rieffel's quantum Gromov-Hausdorff distance, and moreover, form a continuous fami…
A survey of the Preservation of Symmetries by the Dual Gromov-Hausdorff Propinquity
Frederic Latremoliere
We survey the symmetry preserving properties for the dual propinquity, under natural non-degeneracy and equicontinuity conditions. These properties are best formulated using the no…