The Bulk-Edge Correspondence for the Quantum Hall Effect in Kasparov Theory

Authors

Christopher J. Bourne, University of WollongongFollow
Alan L. Carey, University of Wollongong
Adam C. Rennie, University of WollongongFollow

RIS ID

101958

Publication Details

Bourne, C. J., Carey, A. L. & Rennie, A. C. (2015). The Bulk-Edge Correspondence for the Quantum Hall Effect in Kasparov Theory. Letters in Mathematical Physics, 105 (9), 1253-1273.

Abstract

We prove the bulk-edge correspondence in K-theory for the quantum Hall effect by constructing an unbounded Kasparov module from a short exact sequence that links the bulk and boundary algebras. This approach allows us to represent bulk topological invariants explicitly as a Kasparov product of boundary invariants with the extension class linking the algebras. This paper focuses on the example of the discrete integer quantum Hall effect, though our general method potentially has much wider applications.