# The Gromov-Hausdorff propinquity for metric Spectral Triples.

@article{Latrmolire2018TheGP, title={The Gromov-Hausdorff propinquity for metric Spectral Triples.}, author={Fr{\'e}d{\'e}ric Latr{\'e}moli{\`e}re}, journal={arXiv: Operator Algebras}, year={2018} }

We define a metric on the class of metric spectral triples, which is null exactly between spectral triples with unitary equivalent Dirac operators and *-isomorphic underlying C*-algebras. This metric dominates the propinquity, and thus implies metric convergence of the {\qcms s} induced by metric spectral triples. In the process of our construction, we also introduce the covariant modular propinquity, as a key component for the definition of the spectral propinquity.

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