Aeppli and Bott-Chern cohomology for bi-generalized Hermitian manifolds and $d^{\prime }{d}^{\prime \prime }$-lemma

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 $(A,d^{\prime },d^{\prime \prime })$, we show that the validity of $d^{\prime }{d}^{\prime \prime }$-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.

15 pages

References in corpus (5)

• Autour de la cohomologie de Bott-Chern
• New aspects of the ddc-lemma
• Generalized Kahler geometry
• Hodge theory and deformations of SKT manifolds
• Generalized Kaehler geometry of instanton moduli spaces

Cited by in corpus (1)

• $E_1$-degeneration and $d^{\prime }{d}^{\prime \prime }$-lemma