Embedding more than 8 symplectic balls in $\mathbb{C}\mathrm{P}^2$
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918519379066880 |
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| author | Anjos, Sílvia Kędra, Jarek Pinsonnault, Martin |
| author_facet | Anjos, Sílvia Kędra, Jarek Pinsonnault, Martin |
| contents | We prove that the space of symplectic embeddings of $n\geq 1$ standard balls into the standard complex projective plane $\mathbb{C}\mathrm{P}^2$ is homotopy equivalent to the configuration space of $n$ points in $\mathbb{C}\mathrm{P}^2$, provided that the sum of the capacities of the balls is strictly less than the symplectic area of a line. Moreover, our techniques suggest that, for $n=9$, there are infinitely many homotopy types of spaces of symplectic ball embeddings, depending on the capacities of the balls. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24161 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Embedding more than 8 symplectic balls in $\mathbb{C}\mathrm{P}^2$ Anjos, Sílvia Kędra, Jarek Pinsonnault, Martin Symplectic Geometry Primary 57K43, Secondary 57R17, 57S05, 57R40 We prove that the space of symplectic embeddings of $n\geq 1$ standard balls into the standard complex projective plane $\mathbb{C}\mathrm{P}^2$ is homotopy equivalent to the configuration space of $n$ points in $\mathbb{C}\mathrm{P}^2$, provided that the sum of the capacities of the balls is strictly less than the symplectic area of a line. Moreover, our techniques suggest that, for $n=9$, there are infinitely many homotopy types of spaces of symplectic ball embeddings, depending on the capacities of the balls. |
| title | Embedding more than 8 symplectic balls in $\mathbb{C}\mathrm{P}^2$ |
| topic | Symplectic Geometry Primary 57K43, Secondary 57R17, 57S05, 57R40 |
| url | https://arxiv.org/abs/2605.24161 |