Topological boundary maps in physics: General theory and applications

2006/05/16 by Johannes Kellendonk, Kellendonk, Johannes, Serge Richard +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics #Topological Materials and Phenomena

paper · pdf · doi:10.48550/arxiv.math-ph/0605048

openalex publication_date 2006/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Spectral properties of Schrödinger operators and time-decay of the wave functions

Cited by

• On the structure of the wave operators in one dimensional potential scattering

Related

• A topological version of Levinson's theorem
• Levinson's theorem: an index theorem in scattering theory
• Use of Topology in physical problems
• Notes from the bulk
• Classical Mechanics on Finite Spaces