The quantum Gromov-Hausdorff propinquity

Frédéric Latrémolière
2015 Transactions of the American Mathematical Society  
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
more » ... ent of a theory of Leibniz Lip-norms over C*algebras.
doi:10.1090/tran/6334 fatcat:sbkmsfv3rvgftnlvplrojoueaa