Symplectic resolutions, Lefschetz property and formality

Abstract

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.

21 pages, no figures

Cited by in corpus (14)

• On formality of Sasakian manifolds
• Resolution of symplectic cyclic orbifold singularities
• Blow-ups and resolutions of strong Kähler with torsion metrics
• Cohomologies of certain orbifolds
• On simply connected K-contact non-Sasakian manifolds
• A compact $G_2$-calibrated manifold with first Betti number $b_1=1$
• Cohomological aspects of non-Kähler manifolds
• Homology Smale-Barden manifolds with K-contact and Sasakian structures
• Desingularisation of orbifolds obtained from symplectic reduction at generic coadjoint orbits
• Complex Symplectic Lie Algebras with Large Abelian Subalgebras
• Hard Lefschetz property of symplectic structures on compact Kaehler manifolds
• Resolution of $4$-dimensional symplectic orbifolds
• A compact non-formal closed $G_2$ manifold with $b_1=1$
• $A_{\infty }$-Minimal Model on Differential Graded Algebras