Boundaries for two - parabolic Schottky groups

The problem can be formulated in a number of equivalent different settings: in 7 terms of the topology and the geometry of hyperbolic three-manifolds, in purely alge8 braic terms, or in a combination of these. Since each of these use terminology that has 9 whose exact meaning has evolved over time, we survey some of the basic terminology 10 for Schottky groups, non-separating disjoint circle groups, noded surfaces and their 11 various representation spaces. This is done in sections 2, 5, 3, and 4 respectively. In 12 the introduction (sections 1.1, 1.2, and 1.3) we state the main theorems taking the lib13 erty of using some terms whose precise definitions are deferred to the later sections. 14 We begin with the algebraic formulation which may be the quickest way to approach 15 the problem. 16