Abstract: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.
| Comments: | 23 pages |
| Subjects: | Symplectic Geometry (math.SG) |
| MSC classes: | Primary 57K43, Secondary 57R17, 57S05, 57R40 |
| Cite as: | arXiv:2605.24161 [math.SG] |
| (or arXiv:2605.24161v1 [math.SG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24161 arXiv-issued DOI via DataCite (pending registration) |
From: Martin Pinsonnault [view email]
[v1]
Fri, 22 May 2026 19:32:21 UTC (28 KB)
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