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Aeppli and Bott-Chern cohomology for bi-generalized Hermitian manifolds and $d'd''$-lemma (1311.4667v2)
Published 19 Nov 2013 in math.DG, math-ph, math.AT, and math.MP
Abstract: We define Aeppli and Bott-Chern cohomology for bi-generalized complex manifolds and show that they are finite dimensional for compact bi-generalized Hermitian manifolds. For totally bounded double complexes $(A, d', d'')$, we show that the validity of $d'd''$-lemma is equivalent to having the same dimension of several cohomology groups. Some calculations of Bott-Chern cohomology groups of some bi-generalized Hermitian manifolds are given.