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 on a marked surfaces S, to study Calabi-Yau-2 (cluster) categories, Calabi-Yau-3 (Fukaya) categories, braid groups for quivers with potential, quadratic differentials and stability conditions.

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