Topology of the Galaxy Distribution in the Hubble Deep Fields

We have studied topology of the distribution of the high redshift galaxiesidentified in the Hubble Deep Field (HDF) North and South. The two-dimensionalgenus is measured from the projected distributions of the HDF galaxies atangular scales from $3.8''$ to $ 6.1''$. We have also divided the samples intothree redshift slices with roughly equal number of galaxies using photometricredshifts to see possible evolutionary effects on the topology. The genus curve of the HDF North clearly indicates clustering of galaxiesover the Poisson distribution while the clustering is somewhat weaker in theHDF South. This clustering is mainly due to the nearer galaxies in the samples.We have also found that the genus curve of galaxies in the HDF is consistentwith the Gaussian random phase distribution with no significant redshiftdependence.Comment: 14 pages, 4 figures, submitted to Ap