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Symplectic resolutions, Lefschetz property and formality |
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| Authors: | Gil R. Cavalcanti,Vicente Muñ oz |
| Affiliation: | a Mathematical Institute, St. Giles 24 - 29, Oxford OX1 3LB, United Kingdom b Departamento de Matemáticas, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain c Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones Científicas, C/ Serrano 113bis, 28006 Madrid, Spain d Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain |
| Abstract: | We introduce a method to resolve a symplectic orbifold(M,ω) into a smooth symplectic manifold  . Then we study how the formality and the Lefschetz property of  are compared with that of (M,ω). We also study the formality of the symplectic blow-up of (M,ω) 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. |
| Keywords: | Symplectic resolutions Symplectic blow-ups Lefschetz property Formality |
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