T-Duality Simplifies Bulk–Boundary Correspondence: Some Higher Dimensional Cases

2015/06/30 by Varghese Mathai, Guo Chuan Thiang · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Boundary (topology) #Duality (order theory) #Graphene research and applications #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Theoretical physics #Topological Materials and Phenomena #cond-mat.mes-hall #hep-th #math-ph #math.DG #math.MP

paper · pdf · doi:10.1007/s00023-016-0505-6

published as Annales Henri Poincare 17(12) 3399-3424 (2016) · 25 pages. To appear in Ann. Henri Poincare

arxiv created 2016/05/02 · openalex publication_date 2016/06/10 · arxiv updated 2016/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Recently we introduced T-duality in the study of topological insulators, and used it to show that T-duality trivialises the bulk-boundary correspondence in 2 dimensions. In this paper, we partially generalise these results to higher dimensions and briefly discuss the 4D quantum Hall effect.

Citations

• T-duality of topological insulators
• Equality of bulk and edge Hall conductance revisited
• Four-Dimensional Quantum Hall Effect with Ultracold Atoms
• K-Theory for Operator Algebras
• The Bulk-Edge Correspondence for the Quantum Hall Effect in Kasparov Theory
• T-Duality for Torus Bundles with H-Fluxes via Noncommutative Topology
• Classification of "Quaternionic" Bloch-bundles: Topological Quantum Systems of type AII
• 生命的体味动人心魄——安徒生《花与赞美诗》赏读
• Real Baum–Connes assembly and T-duality for torus orientifolds
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Non-commutative differential geometry
• Four-Dimensional Quantum Hall Effect in a Two-Dimensional Quasicrystal
• Topological insulators and K-theory

Cited by

• T-duality simplifies bulk–boundary correspondence: the noncommutative case