Topological boundary maps in physics: General theory and applications

Abstract

The material presented here covers two talks given by the authors at the conference Operator Algebras and Mathematical Physics organised in Bucharest in August 2005. The first one was a review given by J. Kellendonk on the relation between bulk and boundary topological invariants in physical systems. In the second talk S. Richard described an application of these ideas to scattering theory. It leads to a topological version of the so-called Levinson's theorem.

19 pages

References in corpus (2)

• Boundary maps for $C^{\ast }$-crossed products with R with an application to the quantum Hall effect
• Gap-labelling for quasi-crystals (proving a conjecture by J. Bellissard)

Cited by in corpus (8)

• The $K$-theoretic bulk-edge correspondence for topological insulators
• Levinson's theorem for Schroedinger operators with point interaction: a topological approach
• On the structure of the wave operators in one dimensional potential scattering
• The topological meaning of Levinson's theorem, half-bound states included
• Index pairings for ${\mathbb{R}}^n$-actions and Rieffel deformations
• On the wave operators and Levinson's theorem for potential scattering in R^3
• Index theorems for Fredholm, semi-Fredholm, and almost periodic operators: all in one example
• New formulae for the Aharonov-Bohm wave operators