Small symplectic caps and embeddings of homology balls in the complex projective plane
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911111705526272 |
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| author | Etnyre, John B. Min, Hyunki Piccirillo, Lisa Roy, Agniva |
| author_facet | Etnyre, John B. Min, Hyunki Piccirillo, Lisa Roy, Agniva |
| contents | We present a handlebody construction of small symplectic caps, and hence of small closed symplectic 4-manifolds. We use this to construct handlebody descriptions of symplectic embeddings of rational homology balls in $\mathbb{C}\mathrm{P}^2$, and thereby provide the first examples of (infinitely many) symplectic handlebody decompositions of a closed symplectic 4-manifold. Our constructions provide a new topological interpretation of almost toric fibrations of $\mathbb{C}\mathrm{P}^2$ in terms of symplectic handlebody decompositions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_16207 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Small symplectic caps and embeddings of homology balls in the complex projective plane Etnyre, John B. Min, Hyunki Piccirillo, Lisa Roy, Agniva Geometric Topology Symplectic Geometry We present a handlebody construction of small symplectic caps, and hence of small closed symplectic 4-manifolds. We use this to construct handlebody descriptions of symplectic embeddings of rational homology balls in $\mathbb{C}\mathrm{P}^2$, and thereby provide the first examples of (infinitely many) symplectic handlebody decompositions of a closed symplectic 4-manifold. Our constructions provide a new topological interpretation of almost toric fibrations of $\mathbb{C}\mathrm{P}^2$ in terms of symplectic handlebody decompositions. |
| title | Small symplectic caps and embeddings of homology balls in the complex projective plane |
| topic | Geometric Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2305.16207 |