Cluster categories for marked surfaces: punctured case
We study the cluster categories arising from marked surfaces (with punctures and non-empty boundaries). By constructing skewed-gentle algebras, we show that there is a bijection between tagged curves and string objects. Applications include interpreting dimensions of $\operatorname{Ext}^1$ as intersection numbers of tagged curves and Auslander-Reiten translation as tagged rotation. An important consequence is that the cluster(-tilting) exchange graphs of such cluster categories are connected.
PDF AbstractCategories
Representation Theory
Geometric Topology
16G20, 18E30, 16E30, 57M50 (primary), 16G70 (secondary)
