The Modular Gromov-Hausdorff Propinquity

By Frederic Pierre Jean Latrémolière. 2013

47 citations recorded by the source corpus.

We introduce a metric on Hilbert modules equipped with a generalized form of a differential structure, thus extending Gromov-Hausdorff convergence theory to vector bundles and quantum vector bundles --- not convergence as total space but indeed as quantum vector bundle. Our metric is new even in the classical picture, and creates a framework for the study of the moduli spaces of modules over C*-algebras from a metric perspective. We apply our construction, in particular, to the continuity of Heisenberg modules over quantum $2$-tori.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/06454a773522c0f2284f22d2f6bcdee35e2b0d45

Citations in the corpus

• Quantum Ultrametrics on AF Algebras and The Gromov-Hausdorff Propinquity (2015, unknown): “sofquasi-Leibniz quantum compact metric spaces for the quantum propinquity and consisting of infinitely many AF algebras, which is a rather notable result. We also note that since the dual propinquity [22] is also a metric up to isometric isomorphism and is dominated by the quantum propinquity, the t”