Symplectic resolutions, Lefschetz property and formality

Details Symplectic resolutions, Lefschetz property and formality Symplectic resolutions, Lefschetz property and formality

2007-10-03

arxiv.org/abs/0710.0731v1

Adv. Math., 218 (2), 2008, 576--599

Mathematics

Symplectic Geometry

21 pages, no figures

Scientific paper

10.1016/j.aim.2008.01.012

We introduce a method to resolve a symplectic orbifold into a smooth symplectic manifold. Then we study how the formality and the Lefschetz property of the symplectic resolution are compared with that of the symplectic orbifold. We also study the formality of the symplectic blow-up of a symplectic orbifold along symplectic submanifolds disjoint from the orbifold singularities. This allows us to construct the first example of a simply connected compact symplectic manifold of dimension 8 which satisfies the Lefschetz property but is not formal, therefore giving a counter-example to a conjecture of Babenko and Taimanov.

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