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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 $Ω$ coincides with the field of dianalytic functions on a Klein surface $K_Ω$. 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 $\mathbb{R}^{n}/\mathsf{Mod}$, where $\mathsf{Mod}$ is a discrete group.