Decorated marked surfaces II: Intersection numbers and dimensions of Homs

Abstract

We study the 3-Calabi-Yau categories $\mathcal{D}$ arising from quivers with potential associated to a decorated marked surface ${\mathbf{S}}_{△}$ introduced by the first author. We prove two conjectures in the prequel, that under a bijection between certain objects in $\mathcal{D}$ and certain arcs in ${\mathbf{S}}_{△}$, the dimensions of morphisms between these objects equal the intersection numbers between the corresponding arcs.

Introduction and Appendix improved

References in corpus (5)

• Calabi-Yau algebras
• Cluster categories for marked surfaces: punctured case
• Deformed Calabi-Yau Completions
• Decorated marked surfaces: spherical twists versus braid twists
• Cotorsion pairs in the cluster category of a marked surface

Cited by in corpus (5)

• Cluster categories for marked surfaces: punctured case
• Decorated marked surfaces: spherical twists versus braid twists
• Topological structure of spaces of stability conditions and topological Fukaya type categories
• Decorated Marked Surfaces: Calabi-Yau categories and related topics
• The braid group for a quiver with superpotential