L_∞-Kuranishi spaces and the moduli space of pseudoholomorphic disks

2025/11/07 by Kim, Taesu
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Holomorphic and Operator Theory #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2511.05206

openalex publication_date 2025/11/07 · openalex created_date 2025/11/11 · openalex updated_date 2026/07/28

Abstract

We show that the moduli space of pseudoholomorphic disks is an example of the L_∞-Kuranishi spaces introduced in \citeKim1, provided that a condition for the existence of a stratification with a system of tubular neighborhoods holds on each chart. With respect to this structure, the forgetful and evaluation maps for the moduli space lift to morphisms between L_∞-Kuranishi spaces.

Citations

• On Darboux theorems for geometric structures induced by closed forms

Related

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• L_∞-algebra of an unobstructed deformation functor
• A new definition of Kuranishi space
• Kuranishi spaces as a 2-category
• Construction of Kuranishi structures on the moduli spaces of pseudo holomorphic disks: II