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Bulk boundary correspondance for quasiperiodic chains

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Bulk boundary correspondance for quasiperiodic chains
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14
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With the possibility to manufacture almost any structure which might exhibit topological phenomena and to control its boundary there is a need to generalise the standard approach to the bulk boundary correspondence which is based on crossed products to more general settings. For the bulk algebra this can be done using the pattern groupoid algebra. What we will focus on is an approach which allows to include boundaries and to construct more flexible half space algebras than in the cases considered so far. Applications to topological pumping will be given.