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We measure the topology of the main galaxy distribution using the SeventhData Release of the Sloan Digital Sky Survey, examining the dependence ofgalaxy clustering topology on galaxy properties. The observational results areused 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 systematicsand cosmic variance. The clustering topology over the smoothing length intervalfrom 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 findsubstantial bias in the topology of galaxy clustering with respect to thepredicted topology of the matter distribution, which varies with luminosity,morphology, color, and the smoothing scale of the density field. Thedistribution of relatively brighter galaxies shows a greater prevalence ofisolated clusters and more percolated voids. Even though early (late)-typegalaxies show topology similar to that of red (blue) galaxies, the morphologydependence of topology is not identical to the color dependence. In particular,the void abundance parameter $A_V$ depends on morphology more strongly than oncolor. We test five galaxy assignment schemes applied to cosmological N-bodysimulations of a $\Lambda$CDM universe to generate mock galaxies: theHalo-Galaxy one-to-one Correspondence model, the Halo Occupation Distributionmodel, and three implementations of Semi-Analytic Models (SAMs). None of themodels reproduces all aspects of the observed clustering topology; thedeviations vary from one model to another but include statistically significantdiscrepancies in the abundance of isolated voids or isolated clusters and theamplitude and overall shift of the genus curve. (Abridged)

Galaxy Clustering Topology in the Sloan Digital Sky Survey Main Galaxy Sample: a Test for Galaxy Formation Models