Involutions of compact Klein surfaces
Let \(X\) be a compact Klein surface and let \(\varphi: X\to X\) be a dianalytic involution. We determine \(\varphi\) up to topological conjugacy by a finite number of invariants mainly connected with the fixed point set of \(\varphi\). These results generalize classical results of F. Klein for Riemann surfaces without boundary and of W. Scherrer for non-orientable surfaces without boundary. We investigate corresponding inclusions between non- Euclidean crystallographic groups and use these to consider the spaces of Teichmüller and moduli spaces of Klein surfaces admitting involutions.
scientific article; zbMATH DE number 126407