Embeddings of symplectic balls into the complex projective plane

2023/07/02 by Sı́lvia Anjos, Anjos, Sílvia, Jarek Kędra +3 · 1 citation
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Geometry and complex manifolds #Algebraic Geometry and Number Theory

paper · doi:10.48550/arxiv.2307.00556

Abstract

We investigate spaces of symplectic embeddings of n≤ 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 PGL(3,ℂ) on the configuration space of n ordered points in CP² with the action of the symplectomorphism group Symp(CP²) on the space of n embedded symplectic balls.

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