On moduli spaces of Riemann surfaces

Abstract

By M_g(m,n) we denote the moduli space of conformal structures on an oriented compact cobordism S_g(m,n) of genus g greater or equal 0 and with m+n greater or equal 0 enumerated, parametrized boundary components of which n are incoming and m are outgoing. The study of these spaces reflects a strong relationship between geometry, topology and mathematical physics. In this thesis, we study (1) the homotopy type of Bödigheimer's harmonic compactification of these moduli spaces (and of variations of these) and (2) the unstable homology of these moduli spaces (and of variations of these).