reduced singular homology

Let \((X,x)\) be a based space, then the reduced singular homology \(\tilde{H}_n\) is defined

\begin{align*} \tilde{H}_n =& \mathrm{coker}(H_n(*) \rightarrow H_n(X,x)) \end{align*}

resp.

\begin{align*} H_n(X,*) \end{align*}