Abstract: The shape of data contains a great deal of information. We apply persistent homology, a tool in topological data analysis, to build summary statistics from the topology of the large-scale structure of the universe at late times. Employing the Quijote simulations, we perform a Fisher forecast and obtain constraints on cosmological parameters and primordial non-Gaussianity amplitudes. The result is that our topological summary is generally more informative compared with conventional 2-point and 3-point statistics, and combining the approaches allows for more constraining power due to breaking parameter degeneracies. We also demonstrate a pipeline for inference.