Holomorphic Approximation of Symplectic Diffeomorphisms for Calogero--Moser Spaces
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910952184610816 |
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| author | Huang, Gaofeng |
| author_facet | Huang, Gaofeng |
| contents | 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 $\mathcal{C}_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08505 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Holomorphic Approximation of Symplectic Diffeomorphisms for Calogero--Moser Spaces Huang, Gaofeng Complex Variables 2020: 32M17 (Primary), 32E30, 32M25 (Secondary) 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 $\mathcal{C}_n$. |
| title | Holomorphic Approximation of Symplectic Diffeomorphisms for Calogero--Moser Spaces |
| topic | Complex Variables 2020: 32M17 (Primary), 32E30, 32M25 (Secondary) |
| url | https://arxiv.org/abs/2404.08505 |