On symplectic fillings of spinal open book decompositions II: Holomorphic curves and classification
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866918425796804608 |
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| author | Lisi, Samuel Van Horn-Morris, Jeremy Wendl, Chris |
| author_facet | Lisi, Samuel Van Horn-Morris, Jeremy Wendl, Chris |
| contents | In this second paper of a two-part series, we prove that whenever a contact 3-manifold admits a uniform spinal open book decomposition with planar pages, its (weak, strong and/or exact) symplectic and Stein fillings can be classified up to deformation equivalence in terms of diffeomorphism classes of Lefschetz fibrations. This extends previous results of the third author to a much wider class of contact manifolds, which we illustrate here by classifying the strong and Stein fillings of all oriented circle bundles with non-tangential $S^1$-invariant contact structures. Further results include new vanishing criteria for the ECH contact invariant and algebraic torsion in SFT, classification of fillings for certain non-orientable circle bundles, and a general "symplectic quasiflexibility" result about deformation classes of Stein structures in real dimension four. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_16330 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On symplectic fillings of spinal open book decompositions II: Holomorphic curves and classification Lisi, Samuel Van Horn-Morris, Jeremy Wendl, Chris Symplectic Geometry Geometric Topology 32Q65, Secondary 57R17 In this second paper of a two-part series, we prove that whenever a contact 3-manifold admits a uniform spinal open book decomposition with planar pages, its (weak, strong and/or exact) symplectic and Stein fillings can be classified up to deformation equivalence in terms of diffeomorphism classes of Lefschetz fibrations. This extends previous results of the third author to a much wider class of contact manifolds, which we illustrate here by classifying the strong and Stein fillings of all oriented circle bundles with non-tangential $S^1$-invariant contact structures. Further results include new vanishing criteria for the ECH contact invariant and algebraic torsion in SFT, classification of fillings for certain non-orientable circle bundles, and a general "symplectic quasiflexibility" result about deformation classes of Stein structures in real dimension four. |
| title | On symplectic fillings of spinal open book decompositions II: Holomorphic curves and classification |
| topic | Symplectic Geometry Geometric Topology 32Q65, Secondary 57R17 |
| url | https://arxiv.org/abs/2010.16330 |