Topology of large-scale structure. IV - Topology in two dimensions
Adrian L. Melott, Alexander P. Cohen, Andrew J S Hamilton, III Gott J. Richard, David H. Weinberg · The Astrophysical Journal · 1989
In a recent series of papers we have developed an algorithm for quantitatively measuring the topology of the large-scale structure of the universe and applied this algorithm to numerical models and to three- dimensional observational data sets. In this paper we show that topological information can be derived from a two-dimensional cross section of a density field, and we give analytic expressions for a Gaussian random field. We demonstrate the application of a two-dimensional numerical algorithm for measuring topology to cross sections of three-dimensional models similar to those examined in previous papers in this series, and we show that the results are understandable by analogy to three-dimensional results. We discuss prospects for applying this method to nearly two-dimensional observational data sets.