
The purpose of this paper is to study an aspect of a topological mirror symmetry on elliptic curves starting from the paper of \textit{A. N. Tyurin} [Izv. Math. 64, No. 2, 363--437 (2000; Zbl 1039.53058)] which compares the moduli spaces of stable bundles and supercycles. The stable bundles of certain topological type are deformed to standard holomorphic bundles on a noncommutative complex torus, along deformation quantization procedure. The authors show that the deformation is mirror symmetric to an irrational rotation algebra and they conclude that a mirror reflexion of a noncommutative complex torus is an elliptic curve equipped with a Kroneker foliation.
Noncommutative geometry (à la Connes), Noncommutative geometry methods in quantum field theory, Kronecker foliation, mirror symmetry, noncommutative complex torus, Noncommutative global analysis, noncommutative residues
Noncommutative geometry (à la Connes), Noncommutative geometry methods in quantum field theory, Kronecker foliation, mirror symmetry, noncommutative complex torus, Noncommutative global analysis, noncommutative residues
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