Decorated Marked Surfaces: Calabi-Yau categories and related topics
Yu Qiu
TL;DR
This survey explores decorated marked surfaces and their role in understanding Calabi-Yau categories, braid groups, and stability conditions in mathematical physics and algebraic geometry.
Contribution
It introduces the decoration $ riangle$ on marked surfaces to unify and study various Calabi-Yau categories and related structures.
Findings
Connections between decorated surfaces and Calabi-Yau categories
Insights into braid groups for quivers with potential
Applications to quadratic differentials and stability conditions
Abstract
This is a survey on the project `Decorated Marked Surfaces', where we introduce the decoration on a marked surfaces , 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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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory