Summary: L. Keen and C. Series [Proc. Lond. Math. Soc., III. Ser. 69, No. 1, 72-90 (1994; Zbl 0807.30031)]analysed the theory of pleating coordinates in the context of the Riley slice of the Schottky space \(\mathcal R\), 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 loc. cit. the enumeration of the possible bending laminations for \(\mathcal R\), complicated in this case by the fact that the associated three manifold has compressible boundary. We correct two complementary errors in the paper cited above, which arose from subtleties of the enumeration, in particular showing that, contrary to the assertion made in loc. cit., the pleating rays, namely the loci in \(\mathcal R\) in which the projective measure class of the bending lamination is fixed, have two connected components.
For the entire collection see [Zbl 0901.00063].