  Several observational and theoretical indications suggest that the initial
mass function (IMF) becomes increasingly top-heavy (i.e., overabundant in
high-mass stars with mass $m > 1M_{\odot}$) with decreasing metallicity and
increasing gas density of the forming object. This affects the evolution of
globular clusters (GCs) owing to the different mass-loss rates and the number
of black holes formed. Previous numerical modeling of GCs usually assumed an
invariant canonical IMF. Using the state-of-the-art $NBODY6$ code, we perform a
comprehensive series of direct $N$-body simulations to study the evolution of
star clusters, starting with a top-heavy IMF and undergoing early gas
expulsion. Utilizing the embedded cluster mass-radius relation of Marks &
Kroupa (2012) for initializing the models, and by varying the degree of
top-heaviness, we calculate the minimum cluster mass needed for the cluster to
survive longer than 12 Gyr. We document how the evolution of different
characteristics of star clusters such as the total mass, the final size, the
density, the mass-to-light ratio, the population of stellar remnants, and the
survival of GCs is influenced by the degree of top-heaviness. We find that the
lifetimes of clusters with different IMFs moving on the same orbit are
proportional to the relaxation time to a power of $x$ that is in the range of
0.8 to 1. The observed correlation between concentration and the mass function
slope in Galactic GCs can be accounted for excellently in models starting with
a top-heavy IMF and undergoing an early phase of rapid gas expulsion.
