Cotorsion pairs in cluster categories of type $A_{\infty }^{\infty }$

Abstract

In this paper, we give a complete classification of cotorsion pairs in a cluster category $\mathcal{C}$ of type $A_{\infty }^{\infty }$ via certain configurations of arcs, called $\tau$-compact Ptolemy diagrams, in an infinite strip with marked points. As applications, we classify $t$-structures and functorially finite rigid subcategories in $\mathcal{C}$, respectively. We also deduce Liu-Paquette's classification of cluster tilting categories of $\mathcal{C}$ and Ng's classification of torsion pairs in the cluster category of type $A_{\infty }$.

arXiv commentFix a typo in Definition 3.5

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