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Application of Semifinite Index Theory to Weak Topological Phases

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2016 MATRIX Annals

Part of the book series: MATRIX Book Series ((MXBS,volume 1))

Abstract

Recent work by Prodan and the second author showed that weak invariants of topological insulators can be described using Kasparov’s KK-theory. In this note, a complementary description using semifinite index theory is given. This provides an alternative proof of the index formulae for weak complex topological phases using the semifinite local index formula. Real invariants and the bulk-boundary correspondence are also briefly considered.

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Acknowledgements

We thank our collaborators, Alan Carey, Johannes Kellendonk, Emil Prodan and Adam Rennie, whose work this builds from. We also thank the anonymous referee, whose careful reading and suggestions have improved the manuscript. We are partially supported by the DFG grant SCHU-1358/6 and C. B. is also supported by an Australian Mathematical Society Lift-Off Fellowship and a Japan Society for the Promotion of Science Postdoctoral Fellowship for Overseas Researchers (no. P16728).

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Authors and Affiliations

  1. Department Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, 91058, Erlangen, Germany

    Chris Bourne & Hermann Schulz-Baldes

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

    Chris Bourne

Authors
  1. Chris Bourne
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  2. Hermann Schulz-Baldes
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Correspondence to Chris Bourne .

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Editors and Affiliations

  1. University of Melbourne, Melbourne, Australia

    Jan de Gier

  2. University of Western Australia, Crawley, Australia

    Cheryl E. Praeger

  3. UCLA, Los Angeles, USA

    Terence Tao

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Bourne, C., Schulz-Baldes, H. (2018). Application of Semifinite Index Theory to Weak Topological Phases. In: de Gier, J., Praeger, C., Tao, T. (eds) 2016 MATRIX Annals. MATRIX Book Series, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-72299-3_10

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