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We determine the low-energy behaviour of the scattering operator oftwo-dimensional Schr\"odinger operators with any type of obstructions at0-energy. We also derive explicit formulas for the wave operators in theabsence of p-resonances, and outline in this case a topological version ofLevinson's theorem.

Scattering operator and wave operators for 2D Schr\"odinger operators with threshold obstructions