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arXiv · 2307.00556

Embeddings of symplectic balls into the complex projective plane

Sílvia Anjos·Jarek Kędra·Martin Pinsonnault
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Abstract

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 $\mathrm{PGL}(3,\mathbb{C})$ on the configuration space of $n$ ordered points in $\mathbf{CP}^2$ with the action of the symplectomorphism group $\mathrm{Symp}(\mathbf{CP}^2)$ on the space of $n$ embedded symplectic balls.

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Sílvia Anjos, Jarek Kędra, Martin Pinsonnault. 2023-07-02. Embeddings of symplectic balls into the complex projective plane. https://arxiv.org/abs/2307.00556

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