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

Tai-Wei Chen, Chung-I Ho, Jyh-Haur Teh

For a double complex $(A,d^{\prime },d^{\prime \prime })$, we show that if it satisfies the $d^{\prime }{d}^{\prime \prime }$-lemma and the spectral sequence $\{E_r^{p,q}\}$ induced by $A$ does not degenerate at $E_0$, then it…