/sci/ - Science & Math

>>15926317
>So [math]\pi_2(B)[/math]
must be isomorphic to Z
right?
no, as we have a short exact sequence [math]\0\mathbb{Z}\to \pi_2(B)\to\mathbb{Z}\to 0[/math] all we know about [math]\pi_2(B) [/math] is that [math]\\pi_2(B)/\mathbb{Z}=\mathbb{Z}$$ please note that this does not imply that [math]\\pi_2(B)=\mathbb{Z}\oplus\mathbb{Z}[/math].
of course, this cannot be non-trivial so your reasoning is correct other than this