Dga Models for Moment-Angle Complexes

A dga model for the integral singular cochains on a moment-angle complex is given by the twisted tensor product of the corresponding Stanley–Reisner ring and an exterior algebra. We present a short proof of this fact and extend it to real moment-angle complexes. We also compare various descriptions of the cohomology rings of these spaces, including one stated without proof by Gitler and López de Medrano.