  We show that mapping class groups associated to all types of real algebraic
curves are virtual duality groups. We also deduce some results about the
orbifold homotopy groups of the moduli spaces of real algebraic curves. We
achieve these results by defining a new complex associated to a not necessarily
orientable surface with boundary called the
$\mathcal{A}\mathcal{B}\mathcal{C}$-complex. This complex encodes the
intersection patterns of isotopy classes of essential simple arcs, boundary
components, and essential simple closed curves. We show that this complex is
homotopy equivalent to an infinite wedge of spheres; its dimension is dependent
on the topological type of the surface.
