Leftings of Möbius groups to matrix groups.
Lifting di-analytic involutions of compact Klein surfaces to extended-Schottky uniformizations
Let S be a compact Klein surface together with a di-analytic involution κ: S → S. The lowest uniformizations of S are those whose deck group is an extended-Schottky group, that is, an extended Kleinian group whose orientation preserving half is a Schottky group. If S is a bordered compact Klein surface, then it is well known that κ can be lifted with respect to a suitable extended-Schottky uniformization of S. In this paper, we complete the above lifting property by proving that if S is a closed...