Let \(T\) be the infinite cyclic group. Show that there are short exact
sequences
$$
\begin{aligned}
&0 \rightarrow H_{q}\left(A_{*}\right)_{T} \rightarrow \mathbb{H}_{q}\left(T ;
A_{*}\right) \rightarrow H_{q-1}\left(A_{*}\right)^{T} \rightarrow 0 \\
&0 \rightarrow H^{q-1}\left(A^{*}\right)_{T} \rightarrow H^{q}\left(T ;
A^{*}\right) \rightarrow H^{q}\left(A^{*}\right)^{T} \rightarrow 0
\end{aligned}
$$
