We investigate the topology of the new Point Source Catalogue Redshift Survey (PSCz) of IRAS galaxies by means of the genus statistic. The survey maps the local Universe with approximately 15000 galaxies over 84.1 per cent of the sky and provides an unprecedented number of resolution elements for the topological analysis. For comparison with the PSCz data we also examine the genus of large N-body simulations of four variants of the cold dark matter cosmogony. The simulations are part of the Virgo project to simulate the formation of structure in the Universe. We assume that the statistical properties of the galaxy distribution can be identified with those of the dark matter particles in the simulations. We extend the standard genus analysis by examining the influence of sampling noise on the genus curve and introducing a statistic able to quantify the amount of phase correlation present in the density field, the amplitude drop of the genus compared to a Gaussian field with identical power spectrum. The results for PSCz are consistent with the hypothesis of random-phase initial conditions. In particular, no strong phase correlation is detected on scales ranging from 10 h^(-1)Mpc to 32 h^(-1)Mpc, whereas there is a positive detection of phase correlation at smaller scales. Among the simulations, phase correlations are detected in all models at small scales, albeit with different strengths. when scaled to a common normalization, the amplitude drop primarily depends on the shape of the power spectrum. We find that the constant bias standard CDM model can be ruled out at high significance because the shape of its power spectrum is not consistent with PSCz. The other CDM models with more large-scale power all fit the PSCz data almost equally well, with a slight preference for a high-density tauCDM model.
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