A Riemann-Roch theorem for the noncommutative two torus (Q478816)
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| Language | Label | Description | Also known as |
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| English | A Riemann-Roch theorem for the noncommutative two torus |
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A Riemann-Roch theorem for the noncommutative two torus (English)
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4 December 2014
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The noncommutative two-torus for \(C^*\)-algebras is considered. Pseudodifferential operators on them are studied. The authors define a spectral triple using the twisted Dolbeault complex. Its index is used to provide the left side of Riemann-Roch's formula. Asymptotic expansions of traces of associated one-parameter operator semigroups are calculated. An analogue of Riemann-Roch's formula is proved. The corresponding curvature term is discussed.
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noncommutative geometry
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Riemann-Roch theorem
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curved noncommutative torus
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heat equation
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