Orateur
Description
While by a result of McDuff the space of symplectic embeddings of a closed 4-ball into an open 4-ball is connected,
the situation for embeddings of cubes 𝐶4=𝐷2×𝐷2 is very different. For instance, for the open ball 𝐵4 of capacity 1, there exists an explicit decreasing sequence 𝑐1,𝑐2,⋯→1/3 such that for 𝑐<𝑐𝑘 there are at least 𝑘 symplectic embeddings of the closed cube 𝐶4(𝑐) of capacity 𝑐 into 𝐵4 that are not isotopic. Furthermore, there are infinitely many non-isotopic symplectic embeddings of 𝐶4(1/3) into 𝐵4.
A similar result holds for several other targets, like the open 4-cube, the complex projective plane, the product of two equal 2-spheres,
or a monotone product of such manifolds and any closed monotone toric symplectic manifold.
The proof uses exotic Lagrangian tori.
This is joint work with Joé Brendel and Grisha Mikhalkin.
