EAN: 9783319293509

BULK AND BOUNDARY INVARIANTS FOR COMPLEX TOPOLO...

This monograph offers an overview of rigorous results on fermionic topological insulators from
the complex classes  namely  those without symmetries or with just a chiral symmetry.
Particular focus is on the stability of the topological invariants in the presence of strong
disorder  on the interplay between the bulk and boundary invariants and on their dependence on
magnetic fields.The first part presents motivating examples and the conjectures put forward by
the physics community  together with a brief review of the experimental achievements. The
second part develops an operator algebraic approach for the study of disordered topological
insulators. This leads naturally to the use of analytical tools from K-theory and
non-commutative geometry  such as cyclic cohomology  quantized calculus with Fredholm modules
and index pairings. New results include a generalized Streda formula and a proof of the
delocalized nature of surface states in topological insulators with non-trivial invariants. The
concluding chapter connects the invariants to measurable quantities and thus presents a refined
physical characterization of the complex topological insulators. This book is intended for
advanced students in mathematical physics and researchers alike.

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