2025/10/07 by Merlin Christ, Christ, Merlin
Computer Science · Mathematics · #18G80 #18N25 (Primary) 13F60 #18N60 #53D37 #57K20 (Secondary) #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2510.05925
openalex publication_date 2025/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
We construct relative 3-Calabi--Yau categories related with higher Teichmüller theory. We further study their corresponding cosingularity categories and the additive categorification of the corresponding cluster algebras. The input for our constructions is a marked surface with boundary and a Dynkin quiver I. In the case of the triangle, these categories have been described in recent work of Keller--Liu. For general surfaces, the categories are constructed via gluing along a perverse schober, categorifying the amalgamation of cluster varieties. The case I=A1 was subject of the prequel paper. We show that the cosingularity category is equivalent to the corresponding Higgs category and to the topological Fukaya category of the marked surface valued in the 1-Calabi--Yau cluster category of type I.