Convergence of Heisenberg Modules over Quantum 2-tori for the Modular Gromov-Hausdorff Propinquity

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 continuous family for the modular propinquity.