The K-Theoretic Bulk–Edge Correspondence for Topological Insulators

@article{Bourne2016TheKB,
  title={The K-Theoretic Bulk–Edge Correspondence for Topological Insulators},
  author={Chris Bourne and Johannes Kellendonk and Adam Graham Rennie},
  journal={Annales Henri Poincar{\'e}},
  year={2016},
  volume={18},
  pages={1833-1866}
}
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 $$C^*$$C… 

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