The K-Theoretic Bulk–Edge Correspondence for Topological Insulators - Probabilités, statistique, physique mathématique
Article Dans Une Revue Annales Henri Poincare Année : 2017

The K-Theoretic Bulk–Edge Correspondence for Topological Insulators

Résumé

We study the application of Kasparov theory to topological insulator systems and the bulk–edge correspondence. We consider observable algebras as modelled by crossed products, where bulk and edge systems may be linked by a short exact sequence. We construct unbounded Kasparov modules encoding the dynamics of the crossed product. We then link bulk and edge Kasparov modules using the Kasparov product. Because of the anti-linear symmetries that occur in topological insulator models, real $C^*$ -algebras and KKO-theory must be used.
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Dates et versions

hal-01555146 , version 1 (08-03-2024)

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Chris Bourne, Johannes Kellendonk, Adam Rennie. The K-Theoretic Bulk–Edge Correspondence for Topological Insulators. Annales Henri Poincare, 2017, 18 (5), pp.1833-1866. ⟨10.1007/s00023-016-0541-2⟩. ⟨hal-01555146⟩
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