Abstract

A conformal automorphism ? S ? S of a closed Riemann surface S of genus ? 2 is said to be of Schottky type if there is a Schottky uniformization of S for which ? lifts. In the case that ? is of Schottky type, we have associated a geometrically finite Kleinian group K, generated by the uniformizing Schottky group G and any of the liftings of ?. We have that K contains G as a normal subgroup and K/G is cyclic. In this note we describe, up to topological equivalence, all possible groups K obtained in this way. Equivalently, if we are given a handlebody M3 of genus p ? 2 and an orientation preserving homeomorphism of finite order ?, then we proceed to describe, up to topological equivalence, the hyperbolic structures of the orbifold M3/? having bounded by below injectivity radius.