On the cluster category of a marked surface without punctures

By Thomas Brustle, Jie Zhang. 2010

121 citations recorded by the source corpus.

We study in this paper the cluster category C(S,M) of a marked surface (S,M). We explicitly describe the objects in C(S,M) as direct sums of homotopy classes of curves in (S,M) and one-parameter families related to closed curves in (S,M). Moreover, we describe the Auslander-Reiten structure of the category C(S,M) in geometric terms and show that the objects without self-extensions in C(S,M) correspond to curves in (S,M) without self-intersections. As a consequence, we establish that every rigid indecomposable object is reachable from an initial triangulation.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2efa91b8fb55f87481312b89e22f92964a953adc

Citations in the corpus

• A geometric model for the derived category of gentle algebras (2018, unknown): “hat the ribbon graph of such a gentle algebra corresponds exactly to the triangulation of the surface. In this context, the indecomposable objects of the associated cluster category were classified in [25] in terms of arcs and closed curves on the surface, and the Auslander-Reiten translation was des”