Embeddings of more than 8 symplectic balls in $\mathbb CP^2$

Abstract: We prove that the space of symplectic embeddings of $n\geq 1$ standard balls, each of capacity at most $\frac{1}{n}$, into the standard complex projective plane $\mathbb CP^2$ is homotopy equivalent to the configuration space of $n$ points in $\mathbb CP^2$. Our techniques also suggest that for every $n \geq 9$, there may exist infinitely many homotopy types of spaces of symplectic ball embeddings.

algebraic geometrydifferential geometrysymplectic geometry

Audience: researchers in the topic

Geometria em Lisboa (IST)

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