IUMJ

Title: Klein foams

Authors: Antonio F. Costas, Sabir M. Gusein-Zade and Sergey M. Natanzon

Issue: Volume 60 (2011), Issue 3, 985-996

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.