A symplectic rigidity theorem (Q5916452)

Let (D,r) denote the closed plane disc of radius r endowed with the canonical symplectic structure. In this note the author proves that \(\prod^{n}_{i=1}(D_ i,r_ i)\) and \(\prod^{n}_{i=1}(D_ i',r_ i')\) are symplectomorphic iff \(r_ i=r_ i'\) for \(i=1,2,...,n.\) The proof is by elementary cohomology considerations, and the fact that \(D_ i\) are closed is essential.