Geometry & Topology Monographs 1 (1998), The Epstein Birthday Schrift, paper no. 14, pages 303-316.

The Riley slice revisited

Yohei Komori, Caroline Series

Abstract. In [4]: `The Riley slice of Schottky space', (Proc. London Math. Soc. 69 (1994), 72-90), 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 [4] 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 [4], which arose from subtleties of the enumeration, in particular showing that, contrary to the assertion made in [4], the pleating rays, namely the loci in R in which the projective measure class of the bending lamination is fixed, have two connected components.

Keywords. Kleinian group, Schottky Group, Riley slice, pleating coordinates

AMS subject classification. Primary: 30F40. Secondary: 32G05.

E-print: arXiv:math.GT/9810194

Submitted: 27 November 1997. Published: 27 October !998.

Notes on file formats

Yohei Komori, Caroline Series
Department of Mathematics, Osaka City University
Osaka 558, Japan

Mathematics Institute, Warwick University Coventry CV4 7AL, England


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