Squeezing deformations in Schottky spaces
Hiro-o Yamamoto · Journal of the Mathematical Society of Japan · 1979
It is well known that any compact Riemann surface can be represented by a Schottky group.The so-called Schottky space, the set of all normalized marked Schottky groups of genus $p$ , has been investigated by many authors.On the other hand, the concept of squeezing deformations of Riemann surfaces is powerful to treat boundaries of spaces of Kleinian groups.If a compact Riemann surface $S$ of genus $p$ is squeezed with respect to a homotopically independent set $\{\alpha_{i}\}_{i=1}^{q}$ of loops on $S$ , then there is a path in the Schottky space of genus $p$ which tends to the boundary of the space.The aim of this paper is to study squeezing deformations of Riemann surfaces by inves- tigating the behavior of the path in the Schottky space.In \S 1 we shall state the definition of squeezing deformations.Some useful properties in the later discussions are proved in \S 2. In \S 4 we define the