Splittings of surfaces

Let F be a compact 2-manifold without boundary and with Euler characteristic x{F) < 0. Only for convenience endow F with a fixed hyperbolic structure, i.e., a discrete, faithful representation of the fundamental group n x F into the space of isometries of hyperbolic 2-space. Teichmller space, ^(F), is the space of all hyperbolic structures on F divided out by conjugation. W. P. Thurston [Thl] showed that ^(F) admits a compactification as a ball of dimension -3# (F). There is a natural identification of the interior of the ball with ^{F) and the boundary of the ball with the space of projective measured geodesic laminations on F (defined below).