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arXiv · 1311.4667

Aeppli and Bott-Chern cohomology for bi-generalized Hermitian manifolds and $d'd''$-lemma

Tai-Wei Chen·Chung-I Ho·Jyh-Haur Teh
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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.

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Tai-Wei Chen, Chung-I Ho, Jyh-Haur Teh. 2013-11-19. Aeppli and Bott-Chern cohomology for bi-generalized Hermitian manifolds and $d'd''$-lemma. https://arxiv.org/abs/1311.4667

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