The homology groups of moduli spaces on non-classical Klein surfaces

We describe the moduli space M-vector±(g,c) of non-classical directed Klein surfaces of genus g=h-c-1 with c≥0 distinguished points as a configuration space B±(h,c) of classes h-slit pairs in C. Based on this model, we prove that M-vector±(g,c) is non-orientable for any g and c and we compute the homology groups of the moduli spaces M-vector±(g,c) for g≤2. (author)