Various aspects of mathematical physics gave rise to what is called $H$-flux and later to $F$-, $Q$- and $R$-flux. $H$-flux can be identified with a closed 3-form; on a Poisson manifold, the `dual´ $R$-flux is a 3-vector field. It is related to an anomaly/failure of the Jacobi identity. As hoped for, that anomaly indicates an $L_\infty$-structure.

I will include an explanation in mathematical terms of what physicists call \emph{flux}.

This is joint work in progress with Andreas Deser and Tom Lada,