McCleary User’s Guide to Spectral Sequences (Errata)

(pg 455) When an element $u\in H_{n-1}(X)$ satisfies $ru=0$ , then, by exactness, there is an element $\mathbf{\bar{u}\in H_n}(X;\mathbb{Z}/r\mathbb{Z})$ with $\partial(\bar{u})=u$ . Should be $H_n$ instead of $H_{n+1}$ .

(pg 458) The first differential is given by $d^1=\boxed{{\text{red}_p}_*\circ\partial}=\beta$ . The order in the printed version is incorrect. Note that the first differential should be $d^1=j\circ k$ for the exact couple.

See also Recommended Books for Spectral Sequences.

Author: mathtuition88

https://mathtuition88.com/ View all posts by mathtuition88

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