Timeline for What is the cokernel of the map $H^2\big(\pi_1(X), \mathbb Z\big) \longrightarrow H^2(X,\mathbb Z).$
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| May 19, 2015 at 11:22 | comment | added | Will Sawin | $H_2(\overline{X}, \mathbb Z)=Hom(\pi_2(X),\mathbb Z)$. So we get a map $H^2(X,\mathbb Z) \to Hom(\pi_2(X),mathbb Z)$. Presumably this is the "obvious" map. Then you can describe this as the group of functions on spheres in $X$ that come from cohomology classes. I'm not sure if that's simpler. | |
| May 19, 2015 at 9:37 | history | answered | abx | CC BY-SA 3.0 |