Decorated Marked Surfaces: Calabi-Yau categories and related topics

Abstract

This is a survey on the project `Decorated Marked Surfaces', where we introduce the decoration $\Delta$ on a marked surfaces $\mathbf{S}$, to study Calabi-Yau-2 (cluster) categories, Calabi-Yau-3 (Fukaya) categories, braid groups for quivers with potential, quadratic differentials and stability conditions.

arXiv commentThis survey is contributed to the proceedings of the 51st Symposium on Ring Theory and Representation Theory (Sep. 2018 @ Okayama)

References in corpus (6)

• Cluster categories for marked surfaces: punctured case
• Decorated marked surfaces: spherical twists versus braid twists
• q-Stability conditions on Calabi-Yau-X categories
• Decorated marked surfaces II: Intersection numbers and dimensions of Homs
• Decorated marked surfaces III: The derived category of a decorated marked surface
• Topological structure of spaces of stability conditions and topological Fukaya type categories