Keen and Series analysed the theory of pleating coordinates in the
context of the Riley slice of Schottky space R, the deformation space of
a genus two handlebody generated by two parabolics. This theory aims to
give a complete description of the deformation space of a holomorphic
family of Kleinian groups in terms of the bending lamination of the
convex hull boundary of the associated three manifold. In this note,
we review the present status of the theory and discuss, more carefully
than in the article by Keen and Series, the enumeration of the possible
bending laminations for R, complicated in this case by the fact that
the associated three manifold has compressible boundary. We correct two
complementary errors in the earlier paper, which arose from subtleties
of the enumeration, in particular showing that, contrary to a previous
assertion, the pleating rays, namely the loci in R in which the
projective measure class of the bending lamination is fixed, have two
connected components.
