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arXiv · 1208.5462

The noncommutative geometry of wire networks from triply periodic surfaces

Ralph M. Kaufmann·Sergei Khlebnikov·Birgit Wehefritz-Kaufmann
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Abstract

We study wire networks that are the complements of triply periodic minimal surfaces. Here we consider the P, D, G surfaces which are exactly the cases in which the corresponding graphs are symmetric and self-dual. Our approach is using the Harper Hamiltonian in a constant magnetic field. We treat this system with the methods of noncommutative geometry and obtain a classification for all the $C^*$ geometries that appear.

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Ralph M. Kaufmann, Sergei Khlebnikov, Birgit Wehefritz-Kaufmann. 2012-08-27. The noncommutative geometry of wire networks from triply periodic surfaces. https://doi.org/10.1088/1742-6596/343/1/012054

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