Strict contactomorphisms are scarce
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912369572052992 |
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| author | Oh, Yong-Geun Savelyev, Yasha |
| author_facet | Oh, Yong-Geun Savelyev, Yasha |
| contents | The notion of non-projectible contact forms on a given compact manifold $M$ is introduced by the first-named author in [Ohb], the set of which he also shows is a residual subset of the set of (coorientable) contact forms, both in the case with a fixed contact structure and in the case without it. In this paper, we prove that for any non-projectible contact form $λ$ the set, denoted by $\text{\rm Cont}^{\text{\rm st}}(M,λ)$, consisting of strict contactomorphisms of $λ$ is a a countable disjoint union of real lines $\mathbb R$, one for each connected component. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16458 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strict contactomorphisms are scarce Oh, Yong-Geun Savelyev, Yasha Symplectic Geometry 53D10, 53D35, 37C05 The notion of non-projectible contact forms on a given compact manifold $M$ is introduced by the first-named author in [Ohb], the set of which he also shows is a residual subset of the set of (coorientable) contact forms, both in the case with a fixed contact structure and in the case without it. In this paper, we prove that for any non-projectible contact form $λ$ the set, denoted by $\text{\rm Cont}^{\text{\rm st}}(M,λ)$, consisting of strict contactomorphisms of $λ$ is a a countable disjoint union of real lines $\mathbb R$, one for each connected component. |
| title | Strict contactomorphisms are scarce |
| topic | Symplectic Geometry 53D10, 53D35, 37C05 |
| url | https://arxiv.org/abs/2504.16458 |