Note on p-divisibility in Bockstein Spectral Sequence

If u\in H_n(X) generates a copy of \mathbb{Z}, then u\notin\ker p^r.

Write u=a+b, where a\in pH_n(X), b\in\ker p^r. Note that since b=u-a\in\ker p^r, hence b=u-a does not generate a copy of \mathbb{Z}. The only way that is possible is when b=u-a=0, i.e u=a.

Author: mathtuition88

https://mathtuition88.com/

Leave a Reply

Fill in your details below or click an icon to log in:

Gravatar
WordPress.com Logo

You are commenting using your WordPress.com account. ( Log Out /  Change )

Google photo

You are commenting using your Google account. ( Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. ( Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. ( Log Out /  Change )

Cancel

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.