The Fricke space of super-Fuchsian groups (Q1093777)

The author studies the moduli space \(M_{g,n}\) of super-Fuchsian groups of signature (g,n) (equivalent classes modulo spinor structure). These groups act in a domain \(H=\{(a,\alpha)\in {\mathbb{C}}^{(1| 1)}:\) \(Im a>0\}\) in the super-space \({\mathbb{C}}^{(1| 1)}\) as Fuchsian groups of signature (g,n) in the upper half-plane. He points out that \(M_{g,n}\cong T_{g,n}/Mod_{g,n}\) where \(T_{g,n}\) is some analogy of Fricke (Teichmüller) space of Fuchsian groups, and it is diffeomorphic to the super-space \({\mathbb{R}}^{(6g+3n-6| 4g+2n-4)}.\) For the case of signature (g,0) see the paper of \textit{M. A. Baranov} and \textit{A. S. Shvarts}, Letters in Zh. Eksp. Teor. Fiz. 42, No.8, 340-342 (1985).