Cluster categories for marked surfaces: punctured case
Representation Theory
2019-02-20 v3 Geometric Topology
Abstract
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 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.
Cite
@article{arxiv.1311.0010,
title = {Cluster categories for marked surfaces: punctured case},
author = {Yu Qiu and Yu Zhou},
journal= {arXiv preprint arXiv:1311.0010},
year = {2019}
}
Comments
Final version, to appear in Compositio Mathematica