Convergence of Spectral Triples on Fuzzy Tori to Spectral Triples on Quantum Tori

Fuzzy tori are finite dimensional C*-algebras endowed with an appropriate notion of noncommutative geometry inherited from ergodic action a closed subgroup the torus, which meant as approximations and more generally, quantum tori. A mean to specify space is by constructing over it spectral triple. We prove in this paper that we can construct triples on fuzzy which, dimension grows infinity under other natural conditions, converge triple tori, sense propinquity. This provides formal assertion indeed, approximate not only metric spaces, but differentiable manifolds—including convergence state spaces dynamics generated Dirac operators triples, sense.