I wanted to compute explicitly what the coninflation map for homology groups does.
Heres the set up: $G$ is an abelian group, $H$ is a subgroup of finite index and $A$ is a $G$-module that has trivial $H$ action so in this case the coinflation should be $$Coinf: H_{1}(G,A) \longrightarrow H_{1}(G/H,A),$$ but im not sure what happens to a 1-cycle under this map. Im thinking of 1-cycles in $H_{1}(G,A)$ as a map from $f:G \rightarrow A$ that is zero almost everywhere and such that $df=\sum_{g} (g^{-1}-1)f(g) =0$. So if I have a 1-cycle $f$ what does the 1-cycle $Coinf(f)$ look like?
Thank you
