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Popovici, Dan; Stelzig, Jonas and Ugarte, Luis (2021): Higher-page Bott-Chern and Aeppli cohomologies and applications. In: Journal für die Reine und Angewandte Mathematik, Vol. 777: pp. 157-194

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For every positive integer r, we introduce two new cohomologies, that we call E-r-Bott-Chern and E-r-Aeppli, on compact complex manifolds. When r = 1, they coincide with the usual Bott-Chem and Aeppli cohomologies, but they are coarser, respectively finer, than these when r >= 2. They provide analogues in the Bott-Chern-Aeppli context of the E-r-cohomologies featuring in the Frolicher spectral sequence of the manifold. We apply these new cohomologies in several ways to characterise the notion of page-(r - 1)-partial derivative(&PARTIAL) over bar;-manifolds that we introduced very recently. We also prove analogues of the Serre duality for these higher-page Bott-Chern and Aeppli cohomologies and for the spaces featuring in the Frolicher spectral sequence. We obtain a further group of applications of our cohomologies to the study of Hermitian-symplectic and strongly Gauduchon metrics for which we show that they provide the natural cohomological framework.

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