SU(2) as the three-sphere
= SU(2) as the three-sphere
{c}
{title2=$SU(2)\cong S^3$}
Every element of $SU(2)$ has the unique form
$$
\begin{pmatrix}z_1&-\overline z_2\\z_2&\overline z_1\end{pmatrix},
\qquad |z_1|^2+|z_2|^2=1.
$$
Thus $SU(2)$ is diffeomorphic to the unit three-sphere in $\mathbb C^2$ and is a <parallelizable manifold>.