Klein Foams

Abstract

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

arXiv comment9 pages