A JSJ-type decomposition theorem for symplectic fillings
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866913850274611200 |
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| author | Christian, Austin Menke, Michael |
| author_facet | Christian, Austin Menke, Michael |
| contents | We establish a JSJ-type decomposition theorem for splitting exact symplectic fillings of contact 3-manifolds along \emph{mixed tori} -- these are convex tori satisfying a particular geometric condition. As an application, we show that if $(M,ξ)$ is obtained from $(S^3,ξ_{\mathrm{std}})$ via Legendrian surgery along a knot which has been stabilized both positively and negatively, then $(M,ξ)$ has a unique exact filling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1807_03420 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | A JSJ-type decomposition theorem for symplectic fillings Christian, Austin Menke, Michael Symplectic Geometry 57R17 We establish a JSJ-type decomposition theorem for splitting exact symplectic fillings of contact 3-manifolds along \emph{mixed tori} -- these are convex tori satisfying a particular geometric condition. As an application, we show that if $(M,ξ)$ is obtained from $(S^3,ξ_{\mathrm{std}})$ via Legendrian surgery along a knot which has been stabilized both positively and negatively, then $(M,ξ)$ has a unique exact filling. |
| title | A JSJ-type decomposition theorem for symplectic fillings |
| topic | Symplectic Geometry 57R17 |
| url | https://arxiv.org/abs/1807.03420 |