Geodesic
$E_1$-degeneration and $d'd''$-lemma
Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 2, pp. 155-162.

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For a double complex $(A, d', d'')$, we show that if it satisfies the $d'd''$-lemma and the spectral sequence $\{E^{p, q}_r\}$ induced by $A$ does not degenerate at $E_0$, then it degenerates at $E_1$. We apply this result to prove the degeneration at $E_1$ of a Hodge-de Rham spectral sequence on compact bi-generalized Hermitian manifolds that satisfy a version of $d'd''$-lemma.
DOI : 10.14712/1213-7243.2015.156
Classification : 53C05, 55T05
Keywords: $\partial\overline{\partial}$-lemma; Hodge-de Rham spectral sequence; $E_1$-degeneration; bi-generalized Hermitian manifold 
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Chen, Tai-Wei; Ho, Chung-I; Teh, Jyh-Haur. $E_1$-degeneration and $d'd''$-lemma. Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 2, pp. 155-162. doi : 10.14712/1213-7243.2015.156. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.156/

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