Let $S:SU(2)\rightarrow SU(2)$ be defined as $S(X)=X^{4}$. Compute the degree of $S$.
Now, $SU(2)$ is homeomorphic to $S^{3}$, so the degree can be taken as:$$ \int_{S^{3}}S^{*}\omega=(\deg S)\int_{S^{3}}\omega$$
where $\omega$ is a nontrivial 3-form on $H^{3}(S^{3})$. Explicitly, I know that this is: $$ \omega=\sum_{i=0}^{k}(-1)^{i}x^{i}dx^{0}\wedge\dots\wedge dx^{i-1}\wedge dx^{i+1}\wedge\dots\wedge dx^{k}$$
where $k=3$. Now, $\int_{S^{3}}\omega$ is equal to $4$ times the volume of $B^{4}$. I am having some trouble computing $\int_{S^{3}}S^{*}\omega$ which would enable me to find $\deg S$.