Embeddings of symplectic balls into the complex projective plane
Published in arxiv.org, 2024
Recommended citation: Sílvia Anjos, Jarek Kędra, Martin Pinsonnault. (2024). "Embeddings of symplectic balls into the complex projective plane." arxiv:2307.00556. https://arxiv.org/abs/2307.00556
We investigate spaces of symplectic embeddings of $n\leq 4$ balls into the complex projective plane. We prove that they are homotopy equivalent to explicitly described algebraic subspaces of the configuration spaces of $n$ points. We compute the rational homotopy type of these embedding spaces and their cohomology with rational coefficients. Our approach relies on the comparison of the action of $\mathrm{PGL}(3,\mathbf{C})$ on the configuration space of $n$ ordered points in $\mathbf{C}P^2$ with the action of the symplectomorphism group $\mathrm{Symp}(\mathbf{C}P^2)$ on the space of n embedded symplectic balls.