Degenerations of the hyperbolic space (Q1107169)

Let \({\mathcal H}^ n(G)\) be the space of discrete faithful representations of a group G in the group of isometries of hyperbolic n-space (the Teichmüller space for \(n=2)\). Morgan and Shalen, motivated by work of Thurston, have shown that \({\mathcal H}^ n(G)\) admits a natural compactification; the new points correspond to isometric actions of G on \({\mathbb{R}}\)-trees (countable increasing unions of metric trees). They use tools from algebraic geometry; in the present nicely written paper a different proof is given remaining in the realm of hyperbolic geometry. An important ingredient is the notion of ``convergence of compact metric spaces'' due to Gromov.