Klein Foams

Klein foams are analogues of Riemann and Klein surfaces with one-dimensional singularities. We prove that the field of dianalytic functions on a Klein foam $\mathrm{\Omega }$ coincides with the field of dianalytic functions on a Klein surface $K_{\mathrm{\Omega }}$. We construct the moduli space of Klein foams and we prove that the set of classes of topologically equivalent Klein foams form an analytic space homeomorphic to ${\mathbb{R}}^n\mathrm{/}\mathsf{M}\mathsf{o}\mathsf{d}$, where $\mathsf{M}\mathsf{o}\mathsf{d}$ is a discrete group.