A $\tau$-Tilting Approach to Dissections of Polygons

Abstract

We show that any accordion complex associated to a dissection of a convex polygon is isomorphic to the support $\tau$-tilting simplicial complex of an explicit finite dimensional algebra. To this end, we prove a property of some induced subcomplexes of support $\tau$-tilting simplicial complexes of finite dimensional algebras.

References in corpus (3)

• Non-kissing complexes and tau-tilting for gentle algebras
• Geometric realizations of the accordion complex of a dissection
• Stokes posets and serpent nests

Cited by in corpus (3)

• Non-kissing complexes and tau-tilting for gentle algebras
• Geometric realizations of the accordion complex of a dissection
• $\tau$-tilting finite gentle algebras are representation-finite