2010/05/31 by Thomas Brüstle, Jie Zhang · 2 citations
Mathematics · #Algebraic structures and combinatorial models #Cluster (spacecraft) #Geometric and Algebraic Topology #Homotopy #Homotopy and Cohomology in Algebraic Topology #Indecomposable module #Object (grammar) #Surface (topology) #math.RT
paper · pdf · doi:10.2140/ant.2011.5.529
published as Algebra and Number Theory, 5 (2011), No. 4, 529-566 · 33 pages, we add a new corollary 1.6 which shows there is a bijection between triangulations of (S,M) and the cluster-tilting objects of C(S,M), and every rigid indecomposable object is reachable from an initial triangulation
arxiv created 2010/06/17 · openalex publication_date 2011/12/21 · arxiv updated 2012/11/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the cluster category [math] of a marked surface [math] without punctures. We explicitly describe the objects in [math] as direct sums of homotopy classes of curves in [math] and one-parameter families related to noncontractible closed curves in [math] . Moreover, we describe the Auslander–Reiten structure of the category [math] in geometric terms and show that the objects without self-extensions in [math] correspond to curves in [math] without self-intersections. As a consequence, we establish that every rigid indecomposable object is reachable from an initial triangulation.