A Schottky group is a free, discrete group of Möbius transformations constructed by pairing disjoint Jordan curves on the Riemann sphere, taking the exterior of one bounded disk to the interior of its partner. For round circles it is classical. Strictly separated defining disks give a Cantor set as the limit set of a Kleinian group. The tangent-disk extension permits parabolic elements and is often called a noded or T-Schottky group; its Kleinian limit set need not be a Cantor set.
A Schottky group is a specific type of group of isometries of hyperbolic space, particularly in the context of hyperbolic geometry. More formally, it can be defined as a free group of isometries of hyperbolic space, which acts on the hyperbolic plane or hyperbolic 3-space.
New to topics? Read the docs here!