Given $a,b \in \mathfrak{su}(4)$ which are taken to generate the whole algebra, consider the following map $V:\mathbb{R}^{2} \rightarrow SU(4)$:
$V : (w_1, w_{2}) \mapsto e^{(a+w_2 b)} e^{(a+w_1 b)}$
How can I find the singularities of this map? By this I mean points $\vec{w}=(w_1,w_2)$ where the pushforward $dV$ fails to be surjective if any exist? If they cannot be explicitly found, then what structure do they possess?
