#### 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

Email: komori@sci.osaka-cu.ac.jp, cms@maths.warwick.ac.uk

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