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The bulk-edge correspondence for the quantum hall effect in Kasparov Theory

Journal Article


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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.

Publication Date


  • 2015

Citation


  • 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.

Scopus Eid


  • 2-s2.0-84938739787

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=5583&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4562

Number Of Pages


  • 20

Start Page


  • 1253

End Page


  • 1273

Volume


  • 105

Issue


  • 9

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.

Publication Date


  • 2015

Citation


  • 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.

Scopus Eid


  • 2-s2.0-84938739787

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=5583&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4562

Number Of Pages


  • 20

Start Page


  • 1253

End Page


  • 1273

Volume


  • 105

Issue


  • 9