Homotopic properties of Kähler orbifolds

Abstract

We prove the formality and the evenness of odd-degree Betti numbers for compact Kähler orbifolds, by adapting the classical proofs for Kähler manifolds. As a consequence, we obtain examples of symplectic orbifolds not admitting any Kähler orbifold structure. We also review the known examples of non-formal simply connected Sasakian manifolds, and produce an example of a non-formal quasi-regular Sasakian manifold with Betti numbers $b_1=0$ and $b_2>1$.

arXiv comment29 pages, no figures. Background material on orbifolds substantially improved. Comments are welcome! arXiv admin note: text overlap with arXiv:1402.6861