Galaxy Clustering Topology in the Sloan Digital Sky Survey Main Galaxy
  Sample: a Test for Galaxy Formation Models
  We measure the topology of the main galaxy distribution using the Seventh
Data Release of the Sloan Digital Sky Survey, examining the dependence of
galaxy clustering topology on galaxy properties. The observational results are
used to test galaxy formation models. A volume-limited sample defined by
$M_r<-20.19$ enables us to measure the genus curve with amplitude of $G=378$ at
$6h^{-1}$Mpc smoothing scale, with 4.8\% uncertainty including all systematics
and cosmic variance. The clustering topology over the smoothing length interval
from 6 to $10 h^{-1}$Mpc reveals a mild scale-dependence for the shift
($\Delta\nu$) and void abundance ($A_V$) parameters of the genus curve. We find
substantial bias in the topology of galaxy clustering with respect to the
predicted topology of the matter distribution, which varies with luminosity,
morphology, color, and the smoothing scale of the density field. The
distribution of relatively brighter galaxies shows a greater prevalence of
isolated clusters and more percolated voids. Even though early (late)-type
galaxies show topology similar to that of red (blue) galaxies, the morphology
dependence of topology is not identical to the color dependence. In particular,
the void abundance parameter $A_V$ depends on morphology more strongly than on
color. We test five galaxy assignment schemes applied to cosmological N-body
simulations of a $\Lambda$CDM universe to generate mock galaxies: the
Halo-Galaxy one-to-one Correspondence model, the Halo Occupation Distribution
model, and three implementations of Semi-Analytic Models (SAMs). None of the
models reproduces all aspects of the observed clustering topology; the
deviations vary from one model to another but include statistically significant
discrepancies in the abundance of isolated voids or isolated clusters and the
amplitude and overall shift of the genus curve. (Abridged)
