THE TOPOLOGY OF LARGE-SCALE STRUCTURE .6. SLICES OF THE UNIVERSE

We have studied the topology of large-scale structure in two observed slices of the universe. Both slices pass through the Coma cluster and their depths are 100 and 230h-1 Mpc. The topology in these slices measured by the genus statistic is basically spongelike with a possible small shift toward a meatball topology. Our topology study shows that the largest void in the CfA slice is divided into two smaller voids by a statistically significant line of galaxies. Gravitational instability models often produce this kind of minor Zel'dovich pancake running through big voids that are bounded by major Zel'dovich pancakes. The topology of toy models like the white noise and bubble models is shown to be inconsistent with that of the observed slices. We have made a large N-body simulation of the biased cold dark matter model and simulated the slices by matching them in selection functions and boundary conditions. The genus curves for these simulated slices are also spongelike and have a small shift in the direction of a meatball topology like those of observed slices.