On symplectic fillings of spinal open book decompositions I: Geometric constructions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| _version_ | 1866908933810028544 |
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| author | Lisi, Samuel Van Horn-Morris, Jeremy Wendl, Chris |
| author_facet | Lisi, Samuel Van Horn-Morris, Jeremy Wendl, Chris |
| contents | A spinal open book decomposition on a contact manifold is a generalization of a supporting open book which exists naturally e.g. on the boundary of a symplectic filling with a Lefschetz fibration over any compact oriented surface with boundary. In this first paper of a two-part series, we introduce the basic notions relating spinal open books to contact structures and symplectic or Stein structures on Lefschetz fibrations, leading to the definition of a new symplectic cobordism construction called spine removal surgery, which generalizes previous constructions due to Eliashberg, Gay-Stipsicz and the third author. As an application, spine removal yields a large class of new examples of contact manifolds that are not strongly (and sometimes not weakly) symplectically fillable. This paper also lays the geometric groundwork for a theorem to be proved in part II, where holomorphic curves are used to classify the symplectic and Stein fillings of contact 3-manifolds admitting a spinal open book with a planar page. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1810_12017 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On symplectic fillings of spinal open book decompositions I: Geometric constructions Lisi, Samuel Van Horn-Morris, Jeremy Wendl, Chris Symplectic Geometry Geometric Topology 32Q65, Secondary 57R17 A spinal open book decomposition on a contact manifold is a generalization of a supporting open book which exists naturally e.g. on the boundary of a symplectic filling with a Lefschetz fibration over any compact oriented surface with boundary. In this first paper of a two-part series, we introduce the basic notions relating spinal open books to contact structures and symplectic or Stein structures on Lefschetz fibrations, leading to the definition of a new symplectic cobordism construction called spine removal surgery, which generalizes previous constructions due to Eliashberg, Gay-Stipsicz and the third author. As an application, spine removal yields a large class of new examples of contact manifolds that are not strongly (and sometimes not weakly) symplectically fillable. This paper also lays the geometric groundwork for a theorem to be proved in part II, where holomorphic curves are used to classify the symplectic and Stein fillings of contact 3-manifolds admitting a spinal open book with a planar page. |
| title | On symplectic fillings of spinal open book decompositions I: Geometric constructions |
| topic | Symplectic Geometry Geometric Topology 32Q65, Secondary 57R17 |
| url | https://arxiv.org/abs/1810.12017 |