On the topology of loops of contactomorphisms and Legendrians in non-orderable manifolds
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911900548202496 |
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| author | Hernández-Corbato, Luis Martínez-Aguinaga, Javier |
| author_facet | Hernández-Corbato, Luis Martínez-Aguinaga, Javier |
| contents | We study the global topology of the space $\mathcal L$ of loops of contactomorphisms of a non-orderable closed contact manifold $(M^{2n+1}, α)$. We filter $\mathcal L$ by a quantitative measure of the ``positivity'' of the loops and describe the topology of $\mathcal L$ in terms of the subspaces of the filtration. In particular, we show that the homotopy groups of $\mathcal L$ are subgroups of the homotopy groups of the subspace of positive loops $\mathcal L^+$. We obtain analogous results for the space of loops of Legendrian submanifolds in $(M^{2n+1}, α)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01148 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the topology of loops of contactomorphisms and Legendrians in non-orderable manifolds Hernández-Corbato, Luis Martínez-Aguinaga, Javier Symplectic Geometry Differential Geometry Geometric Topology Primary: 53D10. Secondary: 53D22, 53D35 We study the global topology of the space $\mathcal L$ of loops of contactomorphisms of a non-orderable closed contact manifold $(M^{2n+1}, α)$. We filter $\mathcal L$ by a quantitative measure of the ``positivity'' of the loops and describe the topology of $\mathcal L$ in terms of the subspaces of the filtration. In particular, we show that the homotopy groups of $\mathcal L$ are subgroups of the homotopy groups of the subspace of positive loops $\mathcal L^+$. We obtain analogous results for the space of loops of Legendrian submanifolds in $(M^{2n+1}, α)$. |
| title | On the topology of loops of contactomorphisms and Legendrians in non-orderable manifolds |
| topic | Symplectic Geometry Differential Geometry Geometric Topology Primary: 53D10. Secondary: 53D22, 53D35 |
| url | https://arxiv.org/abs/2406.01148 |