A topological version of Levinson’s theorem is presented. Its proof relies on a C*-algebraic framework which is introduced in detail. Various scattering systems are considered in this framework, and more coherent explanations for corrections due to threshold effects or for a regularization procedure are provided. Potential scattering, point interactions, Friedrichs’ model and Aharonov–Bohm’s operators are some of the examples we have presented. Every concept that we have from scattering theory or from K-theory is introduced from scratch.
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