The genus curve of the Abell clusters

We study the topology of large-scale structure through a genus curve measurement of the recent Abell catalog redshift survey of Postman, Huchra, & Geller (1992). The structure is found to be spongelike near median 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 hypothesis of Gaussian random phase initial conditions. The amplitude of the genus curve corresponds to a power-law spectrum with index n = 0.21^+0.43_-0.47 on scales of 48h^-1 Mpc or to a cold dark matter power spectrum with Ωh = 0.36^+0.46_-0.17.