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Application of Semifinite Index Theory to Weak Topological Phases

  • Chris Bourne
  • Hermann Schulz-Baldes
Chapter
Part of the MATRIX Book Series 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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Notes

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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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department MathematikFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany
  2. 2.Advanced Institute for Materials ResearchTohoku UniversitySendaiJapan

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