We prove the formality and the evenness of odd-degree Betti numbers for compact K"ahler orbifolds, by adapting the classical proofs for K"ahler manifolds. As a consequence, we obtain examples of symplectic orbifolds not admitting any K"ahler orbifold structure. We also review the known examples of non-formal simply connected Sasakian manifolds, and we produce examples of formal simply connected Sasakian manifolds with second Betti number b2≠0.
Homotopic properties of Kähler orbifolds
Bazzoni G;
2017-01-01
Abstract
We prove the formality and the evenness of odd-degree Betti numbers for compact K"ahler orbifolds, by adapting the classical proofs for K"ahler manifolds. As a consequence, we obtain examples of symplectic orbifolds not admitting any K"ahler orbifold structure. We also review the known examples of non-formal simply connected Sasakian manifolds, and we produce examples of formal simply connected Sasakian manifolds with second Betti number b2≠0.
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