Mutation of torsion pairs in triangulated categories and its geometric realization

Yu Zhou, Bin Zhu

Published 2011-05-18, updated 2017-06-30Version 2

We introduce and study mutation of torsion pairs, as a generalization of mutation 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. A geometric realization of mutation of torsion pairs in the cluster category of type $A_n$ or $A_{\infty}$ is given via rotation of Ptolemy diagrams.