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

Chris Bourne, Alan L. Carey, Adam Rennie

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1253-1273
Number of pages21
JournalLetters in Mathematical Physics
Issue number9
Publication statusPublished - 2015 Sept 6
Externally publishedYes


  • Bulk-edge correspondence
  • KK-theory
  • quantum Hall effect
  • spectral triples

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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