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The quantum Gromov-Hausdorff propinquity


Author: Frédéric Latrémolière
Journal: Trans. Amer. Math. Soc. 368 (2016), 365-411
MSC (2010): Primary 46L89, 46L30, 58B34
DOI: https://doi.org/10.1090/tran/6334
Published electronically: May 22, 2015
MathSciNet review: 3413867
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Abstract: We introduce the quantum Gromov-Hausdorff propinquity, a new distance between quantum compact metric spaces, which extends the Gromov-Hausdorff distance to noncommutative geometry and strengthens Rieffel's
quantum Gromov-Hausdorff distance and Rieffel's proximity by making
*-isomorphism a necessary condition for distance zero, while being well adapted to Leibniz seminorms. This work offers a natural solution to the long-standing problem of finding a framework for the development of a theory of Leibniz Lip-norms over C*-algebras.


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Additional Information

Frédéric Latrémolière
Affiliation: Department of Mathematics, University of Denver, Denver, Colorado 80208
Email: frederic@math.du.edu

DOI: https://doi.org/10.1090/tran/6334
Keywords: Noncommutative metric geometry, quantum Gromov-Hausdorff distance, Monge-Kantorovich distance, quantum metric spaces, Lip-norms, compact C*-metric spaces, Leibniz seminorms, quantum tori, finite dimensional approximations.
Received by editor(s): November 6, 2013
Published electronically: May 22, 2015
Article copyright: © Copyright 2015 American Mathematical Society