The quantum Gromov-Hausdorff propinquity

Latrémolière, Frédéric

doi:10.1090/tran/6334

The quantum Gromov-Hausdorff propinquity
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by Frédéric Latrémolière PDF

Trans. Amer. Math. Soc. 368 (2016), 365-411 Request permission

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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