Various aspects of mathematical physics gave rise to what is called $H$-flux and later to
$f$-, $Q$- and $R$-flux.
On a manifold, $H$-flux can be identified with a closed 3-form.
Given a bivector field $\rho$, the $R$-flux `dual' to $H$ is a 3-vector field,
related to an anomaly/failure of the Jacobi identity.
\p
That anomaly hints at curved and
$L_\infty$-structures
which we investigate further.
will include an explanation in mathematical terms of what physicists call \emph{flux}.
This is work \emph{in progress} with
Andreas Deser and \\ Tom Lada.