  Does the IMF vary? Is it significantly different in metal-rich environments
than in metal-poor ones? Theoretical work predicts this to be the case. But in
order to provide robust empirical evidence for this, the researcher must
understand all possible biases affecting the derivation of the stellar mass
function. Apart from the very difficult observational challenges, this turns
out to be highly non-trivial relying on an exact understanding of how stars
evolve, and how stellar populations in galaxies are assembled dynamically and
how individual star clusters and associations evolve. N-body modelling is
therefore an unavoidable tool in this game: the case can be made that without
complete dynamical modelling of star clusters and associations any statements
about the variation of the IMF with physical conditions are most probably
wrong. The calculations that do exist demonstrate time and again that the IMF
is invariant: There exists no statistically meaningful evidence for a variation
of the IMF from metal-poor to metal-rich populations. This means that currently
existing star-formation theory fails to describe the stellar outcome. Indirect
evidence, based on chemical evolution calculations, however indicate that
extreme star-bursts that assembled bulges and elliptical galaxies may have had
a top-heavy IMF.
