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The K-Theoretic Bulk–Edge Correspondence for Topological Insulators

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Abstract

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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Authors and Affiliations

  1. Advanced Institute of Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan

    Chris Bourne

  2. Mathematical Sciences Institute, Australian National University, Canberra, ACT, 0200, Australia

    Chris Bourne

  3. School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, 2522, Australia

    Chris Bourne & Adam Rennie

  4. Department Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstraße 11, 91058, Erlangen, Germany

    Chris Bourne

  5. CNRS UMR 5208, Institut Camille Jordan, Université Claude Bernard Lyon 1, Université de Lyon, 69622, Villeurbanne, France

    Johannes Kellendonk

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  1. Chris Bourne
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  2. Johannes Kellendonk
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Correspondence to Johannes Kellendonk.

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Communicated by Jean Bellissard.

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Bourne, C., Kellendonk, J. & Rennie, A. The K-Theoretic Bulk–Edge Correspondence for Topological Insulators. Ann. Henri Poincaré 18, 1833–1866 (2017). https://doi.org/10.1007/s00023-016-0541-2

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