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We introduce and study mutation of torsion pairs, as a generalization ofmutation of cluster tilting objects, rigid objects and maximal rigid objects.It is proved that any mutation of a torsion pair is again a torsion pair. Ageometric realization of mutation of torsion pairs in the cluster category oftype $A_n$ or $A_{\infty}$ is given via rotation of Ptolemy diagrams.

Mutation of torsion pairs in triangulated categories and its geometric realization