THE GENUS CURVE OF THE ABELL CLUSTERS

We study the topology of large-scale structure through a genus curve m easurement of the recent Abell catalog redshift survey of Postman, Huc hra, and Geller (1992). The structure is found to be spongelike near m edian density and to exhibit isolated superclusters and voids at high and low densities, respectively. The genus curve shows a slight shift toward ''meatball'' topology, but remains consistent with the hypothes is of Gaussian random phase initial conditions. The amplitude of the g enus curve corresponds to a power-law spectrum with index n=0.21(-0.47 )(+0.43) on scales of 48h(-1) Mpc or to a cold dark matter power spect rum with Omega h= 0.36(-0.17)(+0.46).