Generalization of Weinstein's Morphism
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908668534980608 |
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| author | Pedroza, Andrés |
| author_facet | Pedroza, Andrés |
| contents | We introduce a generalization of Weinstein's morphism, defined on π_{2k-1}(Ham(M,ω)) for 1 < k \leq n, where (M,ω) is a 2n-dimensional symplectic manifold. Using this morphism, we show that for n > 1 and 1 < k \leq n, the homotopy groups π_{2k-1}(Ham(CP^n,ω_{FS})) and π_{2k-1}(Ham(\tilde CP^n,\tildeω_ρ)) are nontrivial. Here, (\tilde CP^n,\tildeω_ρ) denotes the symplectic one-point blow-up of (CP^n,ω_FS) of weigh ρ. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16914 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalization of Weinstein's Morphism Pedroza, Andrés Symplectic Geometry Primary: 57S05, 53D35 Secondary: 57R17, 53D05 We introduce a generalization of Weinstein's morphism, defined on π_{2k-1}(Ham(M,ω)) for 1 < k \leq n, where (M,ω) is a 2n-dimensional symplectic manifold. Using this morphism, we show that for n > 1 and 1 < k \leq n, the homotopy groups π_{2k-1}(Ham(CP^n,ω_{FS})) and π_{2k-1}(Ham(\tilde CP^n,\tildeω_ρ)) are nontrivial. Here, (\tilde CP^n,\tildeω_ρ) denotes the symplectic one-point blow-up of (CP^n,ω_FS) of weigh ρ. |
| title | Generalization of Weinstein's Morphism |
| topic | Symplectic Geometry Primary: 57S05, 53D35 Secondary: 57R17, 53D05 |
| url | https://arxiv.org/abs/2511.16914 |