2013ApJS..209...19C

We present measurements of the genus topology of luminous red galaxies (LRGs) from the Sloan Digital Sky Survey (SDSS) Data Release 7 catalog, with unprecedented statistical significance. To estimate the uncertainties in the measured genus, we construct 81 mock SDSS LRG surveys along the past light cone from Horizon Run 3, one of the largest N-body simulations to date, which evolved 72x10³ particles in a 10,815 h^–1 Mpc box. After carefully modeling and removing all known systematic effects due to finite pixel size, survey boundary, radial and angular selection functions, shot noise, and galaxy biasing, we find that the observed genus amplitude reaches 272 at a 22 h^–1 Mpc smoothing scale, with an uncertainty of 4.2%; the estimated error fully incorporates cosmic variance. This is the most accurate constraint on the genus amplitude to date and significantly improves on our previous results. In particular, the shape of the genus curve agrees very well with the mean topology of the SDSS LRG mock surveys in a Λ cold dark matter universe. However, comparison with simulations also shows small deviations of the observed genus curve from the theoretical expectation for Gaussian initial conditions. While these discrepancies are mainly driven by known systematic effects such as shot noise and redshift-space distortions, they do contain important cosmological information on the physical effects connected with galaxy formation, gravitational evolution, and primordial non-Gaussianity. We address the key role played by systematics on the genus curve and show how to accurately correct for their effects to recover the topology of the underlying matter. A future work will provide an interpretation of these deviations in the context of the local model of non-Gaussianity.