Geodesic
Heisenberg Modules over Quantum 2-tori are Metrized Quantum Vector Bundles
Canadian journal of mathematics, Tome 72 (2020) no. 4, pp. 1044-1081

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The modular Gromov–Hausdorff propinquity is a distance on classes of modules endowed with quantum metric information, in the form of a metric form of a connection and a left Hilbert module structure. This paper proves that the family of Heisenberg modules over quantum two tori, when endowed with their canonical connections, form a family of metrized quantum vector bundles, as a first step in proving that Heisenberg modules form a continuous family for the modular Gromov–Hausdorff propinquity.
DOI : 10.4153/S0008414X19000166
Mots-clés : noncommutative metric geometry, Gromov–Hausdorff convergence, Monge-Kantorovich distance, quantum metric space, Lip-norm, D-norm, Hilbert module, noncommutative connection, noncommutative Riemannian geometry, unstable K-theory 
Latrémolière, Frédéric. Heisenberg Modules over Quantum 2-tori are Metrized Quantum Vector Bundles. Canadian journal of mathematics, Tome 72 (2020) no. 4, pp. 1044-1081. doi: 10.4153/S0008414X19000166
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     pages = {1044--1081},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X19000166/}
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