One example: The sphere $S^{n+m+1}$ is the join of $S^n*S^m$of $S^n$ and $S^m$, so having $S^1$ act on each of these the factors you get an action on the former.$S^{n+m+1}$.
One example: The sphere $S^{n+m+1}$ is the join of $S^n$ and $S^m$, so having $S^1$ act on each of these you get an action on the former.