Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
I tried working out the explicit formula (using the connecting homomorphism), and it seems that it is indeed $\beta_r[c\otimes 1]=[\frac{1}{p^r}\partial c\otimes 1]$. If anyone finds a mistake, please alert me, thanks.
@MarkGrant Thanks. But I thought it is the coefficient sequence $\mathbb{Z}/p^r\to\mathbb{Z}/p^{2r}\to\mathbb{Z}/p^r$ instead? (pg 460 McCleary's book)
@JohnPalmieri Just to check regarding the dimension. Is the following true: if there is one summand $\mathbb{Z}/p$ in $d^r E^r_n$, then there is one summand $\mathbb{Z}/p^r$ in $H_{n-1}(X)$. Is that correct? Thanks!
