Holomorphic Approximation of Symplectic Diffeomorphisms for Calogero--Moser Spaces

Gaofeng Huang

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arXiv · 2404.08505

Holomorphic Approximation of Symplectic Diffeomorphisms for Calogero--Moser Spaces

Gaofeng Huang

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Abstract

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

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Gaofeng Huang. 2024-04-12. Holomorphic Approximation of Symplectic Diffeomorphisms for Calogero--Moser Spaces. https://arxiv.org/abs/2404.08505

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