Non Commutative Geometry of Tilings and Gap Labelling

  title={Non Commutative Geometry of Tilings and Gap Labelling},
  author={J. Kellendonk},
To a given tiling a non commutative space and the corresponding C∗-algebra are constructed. This includes the definition of a topology on the groupoid induced by translations of the tiling. The algebra is also the algebra of observables for discrete models of one or many particle systems on the tiling or its periodic identification. Its scaled ordered K0-group furnishes the gap labelling of Schrödinger operators. The group is computed for one dimensional tilings and Cartesian products thereof… CONTINUE READING
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