arXiv subjects
Publications and source records attributed to Pablo Arés Gastesi.
This paper contains some results about Teichmüller spaces of non-orientable surfaces (Klein surfaces). We prove several theorems giving isomorphisms between deformation spaces of Klein surfaces. These results show the similarity between the deformation theory of Klein surfaces, and the theory of Riemann surfaces. We also use the results of I. Kra to give explicit examples of deformation spaces of compact Klein surfaces.
In this paper we parametrize the Teichmüller spaces of constructible Koebe groups, that is Kleinian group that arise as covering of $2-$orbifolds determined by certain normal subgroups of their fundamental groups. We also study the covering spaces of the Teichmüller spaces of those Koebe groups. Finally we prove an isomorphisms theorem similar to the Bers-Greenberg theorem for Fuchsian groups. Our method yields a technique to compute explictly generators of Koebe groups, possibly by programming a computer.
In this paper we will use b-groups to construct coordinates for the Teichmüller spaces of 2-orbifolds. The main technical tool is the parametrization of triangle groups, which allows us to compute explicitly formulæ for generators of b-groups uniformizing orbifolds. In this way, we obtain a technique to pass from the abstract objects of deformation spaces to concrete calculations with Möbius transformations. We explore this computational character of our work by finding the expressions of certain classical isomorphisms between Teichmüller spaces.