Probing Large Scale Structure using Percolation and Genus Curves
  We study topological properties of large scale structure in a set of scale free N-body simulations using the genus and percolation curves as topological characteristics. Our results show that as gravitational clustering advances, the density field shows an increasingly pronounced departure from Gaussianity reflected in the changing shape of the percolation curve and the changing amplitude and shape of the genus curve. Both genus and percolation curves differentiate between the connectedness of overdense and underdense regions if plotted against the density. When plotted against the filling factor the percolation curve alone retains this property. The genus curve shows a pronounced decrease in amplitude caused by phase correlations in the non-linear regime. Both genus and percolation curves provide complementary probes of large scale structure topology and can be used to discriminate between models of structure formation and the analysis of observational data such as galaxy catalogs and MBR maps. 
Varun Sahni (IUCAA), B.S. Sathyaprakash (Caltech and UWCC) and   S.F.Shandarin (Kansas)