  We measure the topology of volume-limited galaxy samples selected from a
parent sample of 314,050 galaxies in the Sloan Digital Sky Survey(SDSS), which
is now complete enough to describe the fully three-dimensional topology and its
dependence on galaxy properties. We compare the observed genus statistic
G\nu_f) to predictions for a Gaussian random field and to the genus measured
for mock surveys constructed from new large-volume simulations of the LambdaCDM
cosmology. In this analysis we carefully examine the dependence of the observed
genus statistic on the Gaussian smoothing scale R_G from 3.5 to 11 h^-1Mpc and
on the luminosity of galaxies over the range -22.50<M_r<-18.5. The void
multiplicity A_V is less than unity at all smoothing scales. Because A_V cannot
become less than 1 through gravitational evolution, this result provides strong
evidence for biased galaxy formation in low density environments. We also find
clear evidence of luminosity bias of topology within the volume-limited
sub-samples. The shift parameter Delta nu indicates that the genus of brighter
galaxies shows a negative shift toward a ``meatball'' (i.e. cluster-dominated)
topology, while faint galaxies show a positive shift toward a ``bubble'' (i.e.
void-dominated) topology. The transition from negative to positive shift occurs
approximately at the characteristic absolute magnitude M_{r*}=-20.4. Even in
this analysis of the largest galaxy sample to date, we detect the influence of
individual large-scale structures, as the shift parameter Delta nu and cluster
multiplicity A_C reflect (at ~3 sigma) the presence of the Sloan Great Wall and
a X-shaped structure which runs for several hundred Mpc across the survey
volume.
