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We measure the topology (genus) of isodensity contour surfaces in volumelimited subsets of the 1.2 Jy IRAS redshift survey, for smoothing scales$\lambda=4\hmpc$, $7\hmpc$, and $12\hmpc$. At $12\hmpc$, the observed genuscurve has a symmetric form similar to that predicted for a Gaussian randomfield. At the shorter smoothing lengths, the observed genus curve shows amodest shift in the direction of an isolated cluster or ``meatball'' topology.We use mock catalogs drawn from cosmological N-body simulations to investigatethe systematic biases that affect topology measurements in samples of this sizeand to determine the full covariance matrix of the expected random errors. Weincorporate the error correlations into our evaluations of theoretical models,obtaining both frequentist assessments of absolute goodness-of-fit and Bayesianassessments of models' relative likelihoods. We compare the observed topologyof the 1.2 Jy survey to the predictions of dynamically evolved, unbiased,gravitational instability models that have Gaussian initial conditions. Themodel with an $n=-1$, power-law initial power spectrum achieves the bestoverall agreement with the data, though models with a low-density cold darkmatter power spectrum and an $n=0$ power-law spectrum are also consistent. Theobserved topology is inconsistent with an initially Gaussian model that has$n=-2$, and it is strongly inconsistent with a Voronoi foam model, which has anon-Gaussian, bubble topology.Comment: ApJ submitted, 39 pages, LaTeX(aasms4), 12 figures, 1 Tabl

The Topology of Large‐Scale Structure in the 1.2 JyIRASRedshift Survey