Genus and spot density in the COBE DMR rst year anisotropy maps

A statistical analysis of texture on the COBE-DMR rst year sky maps based on the genus and spot number is presented. A generalized 2 statistic is de ned in terms of \observable" quantities: the genus and spot density that would be measured by di erent cosmic observers. This strategy together with the use of Monte Carlo simulations of the temperature uctuations, including all the relevant experimental parameters, represent the main di erence with previous analyses. Based on the genus analysis we nd a strong anticorrelation between the quadrupole amplitude Qrms PS and the spectral index n of the density uctuation power spectrum at recombination of the form Qrms PS = 22:2 1:7 (4:7 1:3) n K for xed n, consistent with previous works. The result obtained based on the spot density is consistent with this Qrms PS (n) relation. In addition to the previous results we have determined, using Monte Carlo simulations, the minimum uncertainty due to cosmic variance for the determination of the spectral index with the genus analysis. This uncertainty is n 0:2.