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Journal of the Korean Mathematical Society
Article . 2006 . Peer-reviewed
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zbMATH Open
Article . 2006
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A TOPOLOGICAL MIRROR SYMMETRY ON NONCOMMUTATIVE COMPLEX TWO-TORI

A topological mirror symmetry on noncommutative complex two-tori
Authors: Kim, Eunsang; Kim, Hoil;

A TOPOLOGICAL MIRROR SYMMETRY ON NONCOMMUTATIVE COMPLEX TWO-TORI

Abstract

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.

Keywords

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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
gold