Homotopic properties of Kähler orbifolds

Giovanni Bazzoni, Indranil Biswas, Marisa Fernández, Vicente Muñoz, Aleksy Tralle

Published 2016-05-10Version 1

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 $b_2\,\not=\,0$.