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Keen and Series analysed the theory of pleating coordinates in the context of the Riley slice of
Schottky space
,
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
,
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
in
which the projective measure class of the bending lamination is fixed, have two
connected components.