A Lagrangian filling for every cluster seed

• 成果类型: Article
• 署名作者: Casals, Roger; Gao, Honghao
• 署名单位: University of California System; University of California Davis; Tsinghua University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01268-y
• 发表日期: 2024
• 页码: 809-868
• 关键词: LEGENDRIAN SUBMANIFOLDS; ALGEBRAS; QUIVERS; CURVES; MODULI; KNOTS

摘要

We show that each cluster seed in the augmentation variety contains an embedded exact Lagrangian filling. This resolves the matter of surjectivity of the map from Lagrangian fillings to cluster seeds. The main new technique to produce these Lagrangian fillings is the construction and study of a quiver with potential associated to curve configurations. We prove that its deformation space is trivial and show how to use it to manipulate Lagrangian fillings with L \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{L}$\end{document} -compressing systems via Lagrangian disk surgeries.