Mixed tori in contact surgery diagrams
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917033836281856 |
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| author | Christian, Austin Shah, Tanushree |
| author_facet | Christian, Austin Shah, Tanushree |
| contents | We develop a diagrammatic framework for applying the symplectic JSJ decomposition to exact/weak symplectic fillings of 3-dimensional contact manifolds. Namely, we apply the symplectic JSJ decomposition to a contact surgery diagram for some $(Y,ζ)$, producing a finite collection of contact manifolds, also described diagrammatically, whose exact/weak symplectic fillings determine those of $(Y,ζ)$. We apply this technique to recover known symplectic filling classifications for certain lens spaces and torus bundles, and also to provide an algorithm for classifying the exact/weak symplectic fillings of a large class of plumbed 3-manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19580 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mixed tori in contact surgery diagrams Christian, Austin Shah, Tanushree Geometric Topology Symplectic Geometry 57K33 We develop a diagrammatic framework for applying the symplectic JSJ decomposition to exact/weak symplectic fillings of 3-dimensional contact manifolds. Namely, we apply the symplectic JSJ decomposition to a contact surgery diagram for some $(Y,ζ)$, producing a finite collection of contact manifolds, also described diagrammatically, whose exact/weak symplectic fillings determine those of $(Y,ζ)$. We apply this technique to recover known symplectic filling classifications for certain lens spaces and torus bundles, and also to provide an algorithm for classifying the exact/weak symplectic fillings of a large class of plumbed 3-manifolds. |
| title | Mixed tori in contact surgery diagrams |
| topic | Geometric Topology Symplectic Geometry 57K33 |
| url | https://arxiv.org/abs/2510.19580 |