Metrized Quantum Vector Bundles over Quantum Tori Built from Riemannian Metrics and Rosenberg's Levi–Civita Connections

Leonard Huang

Department of Mathematics, University of Colorado at Boulder, Campus Box 395, 2300 Colorado Avenue, Boulder, CO 80309-0395, USA

Abstract: We build metrized quantum vector bundles, over a generically transcendental quantum torus, from Riemannian metrics, using Rosenberg's Levi—Civita connections for these metrics. We also prove that two metrized quantum vector bundles, corresponding to positive scalar multiples of a Riemannian metric, have distance zero between them with respect to the modular Gromov–Hausdorff propinquity.

Keywords: quantum torus; generically transcendental; quantum metric space; metrized quantum vector bundle; Riemannian metric; Levi–Civita connection.

MSC: 46L08; 46L57; 46L87; 37A55; 58B34

Received: March 13, 2018; in final form July 21, 2018; Published online July 29, 2018

Language: English

DOI: 10.3842/SIGMA.2018.079

Bibliographic databases:

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ArXiv: 1803.04036