Commutators of flows and fields
The well known formula $[X,Y]=\tfrac12\tfrac{\partial^2}{\partial t^2}|_0 (\Fl^Y_{-t}ø\Fl^X_{-t}ø\Fl^Y_tø\Fl^X_t)$ for vector fields $X$, $Y$ is generalized to arbitrary bracket expressions and arbitrary curves of local diffeomorphisms.
math.DG↗