Title: Heisenberg Modules over Quantum 2-tori are metrized quantum vector bundles,
Abstract: 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.