Hybrid extension of Schottky space

摘要

Various authors including Bers, Chuckrow, Yamamoto, Sato, Gerritzen, Herrlich, Canary et al. have attacked the problem of finding a suitable extension of Schottky space S_g, i.e. the space of conjugacy classes of faithful representations of the abstract free group Γ_g of rank g > 1 in PSL_2(C) such that the image group is a Schottky group. (We refer the reader to [10] for a general introduction to Kleinian groups.) Some of these attempts are based on the fact that Schottky groups are uniformising groups for closed Riemann surfaces together with an additional combinatorial structure (see e.g. [13], [5], [6], [1]) while others draw on the general theory of deformation spaces of Kleinian groups as developed by Bers, Maskit, Thurston et al. (see [3] and the literature cited there).