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Embeddings of symplectic balls into the complex projective plane
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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.
Forward citations
Cited by 2 Pith papers
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On isomorphisms of semi-free Hamiltonian $S^1$-manifolds and fixed point data
Two counterexamples refute Gonzales' fixed-data classification, and a corrected version with rational-surface reduced spaces is proved and shown to preserve Cho's Fano classification.
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Family Seiberg-Witten equation on Kahler surface and $\pi_i(\Symp)$ on multiple-point blow ups of Calabi-Yau surfaces
Infinite generation of some higher homotopy groups of symplectomorphism groups is proved for n-point Kahler blowups of tori, K3 surfaces, and Enriques surfaces with non-resonant Kahler classes.
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