Titlebook: Noncommutative Geometry and Number Theory; Where Arithmetic mee Caterina Consani,Matilde Marcolli Textbook 2006 Vieweg+Teubner Verlag | Spr

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https://doi.org/10.1007/978-3-8348-0352-8Archimedean cohomology; Farey fractions; Formula of Atiyah-Singer; Fractional quantum Hall effect; Hecke

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Noncommutative Geometry and Number Theory978-3-8348-0352-8Series ISSN 0179-2156

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Towards the fractional quantum Hall effect: a noncommutative geometry perspective,ing geometry is Euclidean, we then discuss a model of the fractional quantum Hall effect, which is based on hyperbolic geometry simulating the multi-electron interactions. We derive the fractional values of the Hall conductance as integer multiples of orbifold Euler characteristics. We compare the results with experimental data.

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A twisted Burnside theorem for countable groups and Reidemeister numbers,consequences in Dynamics, while its proof needs rather sophisticated results from Functional and Noncommutative Harmonic Analysis..We begin a discussion of the general case (which needs another definition of the dual object). It will be the subject of a forthcoming paper..Some applications and examples are presented.

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