Siyuan Yu, Western University
Symplectic embeddings of balls in ℂP² and the generalized configuration space
Let IEmb(B⁴(c),ℂP²) denote the space of unparameterized symplectic embeddings of k balls of capacities (c₁,...,cₖ), where 1 ≤ k ≤ 8. It is known from the work of S. Anjos, J. Li, T.-J. Li, and M. Pinsonnault that the space of capacities decomposes into convex polygons called stability chambers, and that the homotopy type of IEmb(B⁴(c),ℂP²) depends solely on the stability chambers. Based on recent results of M. Entov and M. Verbitsky on Kähler-type embeddings, we show that for 1 ≤ k ≤ 8, IEmb(B⁴(c),ℂP²) is homotopy equivalent to a union of strata F_I of the configuration space of the complex projective plane F(ℂP²,k). The proof relies on constructing an explicit map from the space of Kähler type embeddings to a generalized version of the configuration space that incorporates both configurations of points and compatible complex structures on ℂP².
MC 5417