Genus Statistics for Structure Formation with Topological Effects

We study the efficiency of genus statistics in differentiating betweendifferent models of structure formation. Simple models which reproduce thesalient features of the structure seeded by topological defects are examined.We consider accretion onto static point masses, modeling slow-moving cosmicstring loops or other primordial point-like sources. Filamentary structures andwakes are considered as models of the structures seeded by slow and fast movingstring, respectively. Comparison is made with predictions of genus statisticsfor Gaussian fluctuations and with genus curves obtained by the CfA survey. Ageneric class of density models with wakes and filaments is found to provideresults comparable or better than Gaussian models for this suite of tests.Comment: Compressed (gzip) uuencoded postcript, 36 pages with 13 figures (figure 2 available upon request), submited to the Astrophysical Journal (Part1