Higher-page Bott–Chern and Aeppli cohomologies and applications

Abstract For every positive integer r , we introduce two new cohomologies, that call E r {E_{r}} -Bott–Chern and -Aeppli, on compact complex manifolds. When = 1 {r\kern-1.0pt=\kern-1.0pt1} they coincide with the usual Bott–Chern Aeppli but are coarser, respectively finer, than these when ? 2 {r\geq 2} . They provide analogues in Bott–Chern–Aeppli context of -cohomologies featuring Frölicher spectral sequence manifold. We apply cohomologies several ways to characterise notion page- ( - stretchy="false">) {(r-1)} - ? ? stretchy="false">¯ {\partial\bar{\partial}} -manifolds introduced very recently. also prove Serre duality for higher-page spaces sequence. obtain a further group applications our study Hermitian-symplectic strongly Gauduchon metrics which show natural cohomological framework.