Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics

TL;DR

This paper reviews the use of K-theory and non-commutative geometry to define and connect bulk and boundary topological invariants in complex fermionic topological insulators, linking mathematical theory to physical observables.

Contribution

It provides a comprehensive overview of the mathematical framework for topological invariants in complex topological insulators, emphasizing the bulk-boundary correspondence.

Findings

Establishment of bulk-boundary correspondence using K-theory

Linking topological invariants to physical observables

Mathematical characterization of invariants in complex classes

Abstract

This monograph offers an overview on the topological invariants in fermionic topological insulators from the complex classes. Tools from K-theory and non-commutative geometry are used to define bulk and boundary invariants, to establish the bulk-boundary correspondence and to link the invariants to physical observables.