The K-theoretic bulk-edge correspondence for topological insulators

Authors

Chris Bourne, University of WollongongFollow
Johannes Kellendonk, Claude Bernard University Lyon 1
Adam C. Rennie, University of WollongongFollow

RIS ID

111541

Publication Details

Bourne, C., Kellendonk, J. & Rennie, A. (2017). The K-theoretic bulk-edge correspondence for topological insulators. Annales Henri Poincare, 18 (5), 1833-1866.

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.