Ralph M. Kaufmann, Sergei Khlebnikov, Birgit Wehefritz-Kaufmann
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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http://arxiv.org/abs/1208.5462
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