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E 1 -degeneration and d ' d ' ' -lemma

Tai-Wei ChenChung-I HoJyh-Haur Teh — 2016

Commentationes Mathematicae Universitatis Carolinae

For a double complex ( A , d ' , d ' ' ) , we show that if it satisfies the d ' d ' ' -lemma and the spectral sequence { E r p , q } 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.

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