Fundamental groups of rationally connected symplectic manifolds
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915466306387968 |
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| author | Pieloch, Alex |
| author_facet | Pieloch, Alex |
| contents | We show that the fundamental group of every enumeratively rationally connected closed symplectic manifold is finite. In other words, if a closed symplectic manifold has a non-zero Gromov-Witten invariant with two point insertions, then it has finite fundamental group. We also show that if the spherical homology class associated to such a non-zero Gromov-Witten invariant is holomorphically indecomposable, then the rational second homology of the symplectic manifold has rank one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_07882 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Fundamental groups of rationally connected symplectic manifolds Pieloch, Alex Symplectic Geometry We show that the fundamental group of every enumeratively rationally connected closed symplectic manifold is finite. In other words, if a closed symplectic manifold has a non-zero Gromov-Witten invariant with two point insertions, then it has finite fundamental group. We also show that if the spherical homology class associated to such a non-zero Gromov-Witten invariant is holomorphically indecomposable, then the rational second homology of the symplectic manifold has rank one. |
| title | Fundamental groups of rationally connected symplectic manifolds |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2212.07882 |