Hereditary properties of co-K\"ahler manifolds

Giovanni Bazzoni; Gregory Lupton; John Oprea

doi:10.1016/j.difgeo.2016.11.002

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arXiv · 1311.5675

Hereditary properties of co-K\"ahler manifolds

Giovanni Bazzoni·Gregory Lupton·John Oprea

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Abstract

We show how certain topological properties of co-K{\"a}hler manifolds derive from those of the K\"ahler manifolds which construct them. We go beyond Betti number results and describe the cohomology algebra structure of co-K\"ahler manifolds. As a consequence, we prove that co-K\"ahler manifolds satisfy the Toral Rank Conjecture: $\dim(H^*(M;\mathbb{Q})) \geq 2^r$, for any $r$-torus $T^r$ which acts almost freely on $M$.

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Giovanni Bazzoni, Gregory Lupton, John Oprea. 2013-11-22. Hereditary properties of co-K\"ahler manifolds. https://doi.org/10.1016/j.difgeo.2016.11.002

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