Holomorphic Approximation of Symplectic Diffeomorphisms for Calogero--Moser Spaces

2024/04/12 by Gaofeng Huang, Huang, Gaofeng · 1 citation
Mathematics · #2020: 32M17 (Primary) #32E30 #32M25 (Secondary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Complex Variables (math.CV) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2404.08505

openalex publication_date 2024/04/12 · openalex created_date 2024/04/16 · openalex updated_date 2026/07/28

Abstract

The real Calogero--Moser space C_n^ℝ is a noncompact, totally real submanifold of the complex Calogero--Moser space C_n. We prove that every symplectic diffeomorphism of C_n^ℝ smoothly isotopic to the identity can be approximated in the fine Whitney topology -- the strongest in this context -- by holomorphic symplectic automorphisms of C_n that preserve C_n^ℝ. A key ingredient in our proof is a refined version of the symplectic density property of C_n.

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• Direct Products for the Hamiltonian Density Property

Related

• The Density Property for Calogero--Moser spaces
• Automorphisms and symplectic leaves of Calogero-Moser spaces
• The Density Property for Generalized Calogero--Moser Spaces with Inner Degrees of Freedom
• The Moser isotopy for holomorphic symplectic and C-symplectic structures
• Direct Products for the Hamiltonian Density Property