NDLI: Cluster categories for marked surfaces: punctured case

Content Provider	Scilit
Author	Qiu, Yu Zhou, Yu
Copyright Year	2017
Description	Journal: Compositio Mathematica We study 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.
Ending Page	1819
Starting Page	1779
ISSN	00221295
e-ISSN	15705846
DOI	10.1112/s0010437x17007229
Journal	Compositio Mathematica
Issue Number	9
Volume Number	153
Language	English
Publisher	Wiley-Blackwell
Publisher Date	2017-06-15
Access Restriction	Open
Subject Keyword	Journal: Compositio Mathematica Mathematical Physics Marked Surfaces
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory

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Cluster categories for marked surfaces: punctured case