An 8-dimensional nonformal, simply connected, symplectic manifold (Q2389105)

It is proved that there is a nonformal, simply connected compact symplectic manifold of dimension 8. This is an affirmative answer to a question posed by \textit{I. K. Babenko} and \textit{I. A. Tajmanov} [Sib. Math. J. 41, No. 2, 204--217 (2000); translation from Sib. Mat. Zh. 41, No.~2, 253--269 (2000; Zbl 0972.53051)]. For this purpose a new technique to produce symplectic manifolds is introduced. The authors consider a nonformal, compact symplectic manifold with same dimension and with a symplectic nonfree action of a finite group such that the quotient space is a nonformal orbifold which is simply connected. Then they resolve symplectically the singularities to produce a smooth symplectic manifold satisfying the required properties.