  We measure the three-dimensional topology of large-scale structure in the
Sloan Digital Sky Survey (SDSS). This allows the genus statistic to be measured
with unprecedented statistical accuracy. The sample size is now sufficiently
large to allow the topology to be an important tool for testing galaxy
formation models. For comparison, we make mock SDSS samples using several
state-of-the-art N-body simulations: the Millennium run of Springel et al.
(2005)(10 billion particles), Kim & Park (2006) CDM models (1.1 billion
particles), and Cen & Ostriker (2006) hydrodynamic code models (8.6 billion
cell hydro mesh). Each of these simulations uses a different method for
modeling galaxy formation. The SDSS data show a genus curve that is broadly
characteristic of that produced by Gaussian random phase initial conditions.
Thus the data strongly support the standard model of inflation where Gaussian
random phase initial conditions are produced by random quantum fluctuations in
the early universe. But on top of this general shape there are measurable
differences produced by non-linear gravitational effects (cf. Matsubara 1994),
and biasing connected with galaxy formation. The N-body simulations have been
tuned to reproduce the power spectrum and multiplicity function but not
topology, so topology is an acid test for these models. The data show a
``meatball'' shift (only partly due to the Sloan Great Wall of Galaxies; this
shift also appears in a sub-sample not containing the Wall) which differs at
the 2.5\sigma level from the results of the Millennium run and the Kim & Park
dark halo models, even including the effects of cosmic variance.
