Symplectic nilmanifolds with a symplectic non-free $Z_3$-action

Mathematics – Symplectic Geometry

Scientific paper

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21 pages, no figures; v2. exposition greatly improved

Scientific paper

This paper expands some of the issues of the paper math.SG/0506449. We introduce a new technique to produce symplectic manifolds, by taking a symplectic non-free action of a finite group on a symplectic manifold and resolving symplectically the singularities of the quotient. We also introduce a new type of Massey product to detect non-formality. This allows to show the first example of a non-formal simply connected compact symplectic manifold of dimension 8.

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