An example of degeneration on the noded Schottky space

Sin resume

Origami-Schottky groups

A Kleinian group $K$, with region of discontinuity $\Omega$, is an origami-Schottky group if (i) it contains a Schottky group $\Gamma$ as a finite index subgroup and (ii) $\Omega/K$ is an orbifold of genus one with exactly one conical point. In this paper, we provide a geometrical structural picture of origami-Schottky groups in terms of the Klein-Maskit combination theorems. Examples of Hurwitz translation surfaces in terms of Schottky groups are provided

Schottky Uniformizations of Z22 Actions on Riemann Surfaces

Given a closed Riemann surface S together a group of its conformal automorphisms H _= Z22 , it is known that there are Schottky uniformizations of S realizing H. In this note we proceed to give an explicit Schottky uniformizations for each of all different topological actions of Z22 as group of conformal automorphisms on a closed Riemann surface.Given a closed Riemann surface S together a group of its conformal automor phisms H Z2 , it is known that there are Schottky uniformizations of S real =2 izing H . In this note we proceed to give an explicit Schottky uniformizations for each of all different topological actions of Z2 as group of conformal automor 2 phisms on a closed Riemann surface

Extending finite free actions of surfaces

We prove the existence of finite groups of orientation-preserving homeomorphisms of some closed orientable surface $S$ that act freely and which extends as a group of homeomorphisms of some compact orientable $3$-manifold with boundary $S$, but which cannot extend to a handlebody