We show how certain topological properties of co-Kähler manifolds derive from those of the Kähler manifolds which construct them. We go beyond Betti number results and describe the cohomology algebra structure of co-Kähler manifolds. As a consequence, we prove that co-Kähler manifolds satisfy the Toral Rank Conjecture: dim(H∗(M;Q))≥2r, for any r-torus T which acts almost freely on M.
Hereditary Properties of co-Kähler manifolds
Bazzoni G;
2017-01-01
Abstract
We show how certain topological properties of co-Kähler manifolds derive from those of the Kähler manifolds which construct them. We go beyond Betti number results and describe the cohomology algebra structure of co-Kähler manifolds. As a consequence, we prove that co-Kähler manifolds satisfy the Toral Rank Conjecture: dim(H∗(M;Q))≥2r, for any r-torus T which acts almost freely on M.
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