2014/11/30 by Chris Bourne, Alan L. Carey, Adam Rennie · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Boundary (topology) #Class (philosophy) #Computer science #Electron #Enhanced Data Rates for GSM Evolution #Extension (predicate logic) #Geometry #Integer (computer science) #Mathematical analysis #Mathematics #Physics #Product (mathematics) #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Hall effect #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Sequence (biology) #Theoretical physics #math-ph #math.KT #math.MP #math.OA
paper · pdf · doi:10.1007/s11005-015-0781-y
16 pages. Minor corrections and introduction expanded. To appear in Letters in Mathematical Physics
openalex publication_date 2015/07/08 · arxiv created 2015/07/12 · arxiv updated 2015/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.