The bulk-edge correspondence for the quantum Hall effect in Kasparov theory
Mathematical Physics
2015-07-14 v2 K-Theory and Homology
math.MP
Operator Algebras
Abstract
We prove the bulk-edge correspondence in -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.
Keywords
Cite
@article{arxiv.1411.7527,
title = {The bulk-edge correspondence for the quantum Hall effect in Kasparov theory},
author = {Chris Bourne and Alan L. Carey and Adam Rennie},
journal= {arXiv preprint arXiv:1411.7527},
year = {2015}
}
Comments
16 pages. Minor corrections and introduction expanded. To appear in Letters in Mathematical Physics