Mutation of torsion pairs in discrete cluster categories of Dynkin type A∞

Abstract

Mutation of torsion pairs is a generalization of mutation of cluster tilting subcategories. Torsion pairs and cluster tilting subcategories in Igusa-Todorov cluster categories of type A∞ have been classified by Gratz-Holm-Jørgensen in [12]. In this paper we give a geometric realization of mutation of torsion pairs in discrete cluster categories of Dynkin type A∞ by rotating some combinatorial models in S1. This result generalizes a work of Zhou-Zhu for cluster category of type A∞[28].