  Recent observations of globular clusters (GCs) provide evidence that the
stellar initial mass function (IMF) may not be universal, suggesting
specifically that the IMF grows increasingly top-heavy with decreasing
metallicity and increasing gas density. Non-canonical IMFs can greatly affect
the evolution of GCs, mainly because the high end determines how many black
holes (BHs) form. Here we compute a new set of GC models, varying the IMF
within observational uncertainties. We find that GCs with top-heavy IMFs lose
most of their mass within a few Gyr through stellar winds and tidal stripping.
Heating of the cluster through BH mass segregation greatly enhances this
process. We show that, as they approach complete dissolution, GCs with
top-heavy IMFs can evolve into 'dark clusters' consisting of mostly BHs by
mass. In addition to producing more BHs, GCs with top-heavy IMFs also produce
many more binary BH (BBH) mergers. Even though these clusters are short-lived,
mergers of ejected BBHs continue at a rate comparable to, or greater than, what
is found for long-lived GCs with canonical IMFs. Therefore these clusters,
although they are no longer visible today, could still contribute significantly
to the local BBH merger rate detectable by LIGO/Virgo, especially for sources
with higher component masses well into the BH mass gap. We also report that one
of our GC models with a top-heavy IMF produces dozens of intermediate-mass
black holes (IMBHs) with masses $M>100\,{\rm M_\odot}$, including one with
$M>500\,{\rm M_\odot}$. Ultimately, additional gravitational wave observations
will provide strong constraints on the stellar IMF in old GCs and the formation
of IMBHs at high redshift.
