The object of the research is to bring a quantitative analysis to the study of the topology of the large-scale structure in the universe. A computer program has been developed to measure the topology of the universe and it will be applied to a large number of observational data sets and N-body simulations. The algorithm smoothes the data set, constructs surfaces of constant density (density contours) and measures the topology of the contour surfaces as a function of density enhancement. The preliminary results obtained so far have been quite encouraging. In many models (including those involving cold dark matter) the topology of smoothed constant density enhancement at the present epoch reflects that present in the initial conditions. Models with random phases (as might arise form quantum noise in inflationary cosmologies) have a universal dependence of topology on density enhancement which can be compared with the observations. These studies should provide some important new insights into the nature of the observed topology and its relation to the initial conditions that produced it.
