Cluster categories for marked surfaces: punctured case
By Yu Qiu, Yu Zhou. Compositio Mathematica, 2013
65 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/c2a9b614002f220041f931a6d380c4993766e2ca
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
- C. Geiss
- J. Schröer
- Bernard Leclerc
- Daniel Labardini-Fragoso
- B. Keller
- Osamu Iyama
- Pierre-Guy Plamondon
- I. Reiten
In Nuclear and High Energy Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- The representation type of Jacobian algebras (2013, methodology): “Theorem 7.11 the Jacobian algebra P(Q(τt),S(τt)) is a skewed-gentle algebra. (This follows directly by combining [ABCP, Theorem 2.7] and the example in Section 6.5.2, compare also the recent preprint [QZ].) 7.13. Triangulations without double arrows. As a straightforward corollary of Theorem 7.8 we ”
- A geometric model for the derived category of gentle algebras (2018, unknown): “for the extension spaces were described in terms of crossings of arcs in [33]. These results were then extended to the case where the surface has punctures (that is, marked points in its interior) in [58], and a complete description of indecomposable objects using arcs and closed curves was given in”