Bulk and Boundary Invariants for Complex Topological Insulators

The textbook "Bulk and Boundary Invariants for Complex Topological Insulators" offers a comprehensive analysis of rigorous results regarding fermionic topological insulators from the complex classes. It specifically addresses the stability of topological invariants under strong disorder and investigates the interplay between bulk and boundary invariants, as well as their dependence on magnetic fields. The first half of the book presents motivating examples and conjectures established by the physics community, complemented by a brief overview of experimental achievements. In the second half, an operator-algebraic approach is developed to study disordered topological insulators, incorporating analytical tools from K-theory and non-commutative geometry. New results include a generalized Streda formula and the proof of the delocalized nature of surface states in topological insulators with non-trivial invariants. The concluding chapter connects the invariants with measurable quantities, thus providing a refined physical characterization of complex topological insulators. This book is aimed at advanced students of mathematical physics as well as researchers.