The morphology of galaxy clusters reflects the epoch at which they formed and hence depends on the value of the mean cosmological density , \Omega _ { 0 } .
Recent studies have shown that the distribution of dark matter in clusters can be mapped from analysis of the small distortions in the shapes of background galaxies induced by weak gravitational lensing in the cluster potential .
We construct new statistics to quantify the morphology of clusters which are insensitive to limitations in the mass reconstruction procedure .
By simulating weak gravitational lensing in artificial clusters grown in numerical simulations of the formation of clusters in three different cosmologies , we obtain distributions of a quadrupole statistic which measures global deviations from spherical symmetry in a cluster .
These distributions are very sensitive to the value of \Omega _ { 0 } and , as a result , lensing observations of a small number of clusters should be sufficient to place broad constraints on \Omega _ { 0 } and certainly to distinguish between the extreme values of 0.2 and 1 .