Index theory and noncommutative geometry of topological insulator

Abstract

In this chapter, we report the recent progress in the understanding of the rich mathematical structures of topological insulators in the framework of index theory and noncommutative geometry.

arXiv comment46 pages. arXiv admin note: text overlap with arXiv:1510.08001

References in corpus (16)

• Topological Insulators
• Topological insulators and superconductors
• Topological Insulators in Three Dimensions
• Topological invariants of time-reversal-invariant band structures
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Majorana Zero Modes and Topological Quantum Computation
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Fermion Path Integrals And Topological Phases
• Bulk-edge correspondence for two-dimensional topological insulators
• Twisted equivariant matter
• Equivalent topological invariants of topological insulators
• Controlled topological phases and bulk-edge correspondence
• The $K$-theoretic bulk-edge correspondence for topological insulators
• Cyclic cohomology for graded $C^{\ast ,r}$-algebras and its pairings with van Daele $K$-theory
• The Stiefel--Whitney theory of topological insulators
• Bott--Kitaev periodic table and index theory