Subcritical polarisations of symplectic manifolds have degree one
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866916090079084544 |
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| author | Geiges, Hansjörg Sporbeck, Kevin Zehmisch, Kai |
| author_facet | Geiges, Hansjörg Sporbeck, Kevin Zehmisch, Kai |
| contents | We show that if the complement of a Donaldson hypersurface in a closed, integral symplectic manifold has the homology of a subcritical Stein manifold, then the hypersurface is of degree one. In particular, this demonstrates a conjecture by Biran and Cieliebak on subcritical polarisations of symplectic manifolds. Our proof is based on a simple homological argument using ideas of Kulkarni-Wood. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_02068 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Subcritical polarisations of symplectic manifolds have degree one Geiges, Hansjörg Sporbeck, Kevin Zehmisch, Kai Symplectic Geometry 53D35, 57R17, 57R19, 57R95 We show that if the complement of a Donaldson hypersurface in a closed, integral symplectic manifold has the homology of a subcritical Stein manifold, then the hypersurface is of degree one. In particular, this demonstrates a conjecture by Biran and Cieliebak on subcritical polarisations of symplectic manifolds. Our proof is based on a simple homological argument using ideas of Kulkarni-Wood. |
| title | Subcritical polarisations of symplectic manifolds have degree one |
| topic | Symplectic Geometry 53D35, 57R17, 57R19, 57R95 |
| url | https://arxiv.org/abs/2101.02068 |