The topological type of the Fano surface of a real three-dimensional $M$-cubic

We compute the topological type of the real part of the Fano surface that parametrizes the set of real lines a non-singular real $M$-threefold. When studying Fano surfaces, we use the results and constructions in [3] on the intermediate Jacobian of a three-dimensional complex cubic. We begin by computing the topological type of the real part of the Fano surface that parametrizes the set of real lines on a singular real $M$-cubic with a single simple singular point.