Volume 1 (1998)

Download this article
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
All Volumes
About this Series
Ethics Statement
Purchase Printed Copies
Author Index
ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
MSP Books and Monographs
Other MSP Publications

The Riley slice revisited

Yohei Komori and Caroline Series

Geometry & Topology Monographs 1 (1998) 303–316

DOI: 10.2140/gtm.1998.1.303

arXiv: math.GT/9810194


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.


Kleinian group, Schottky Group, Riley slice, pleating coordinates

Mathematical Subject Classification

Received: 27 November 1997
Published: 27 October 1998

Yohei Komori
Department of Mathematics
Osaka City University
Osaka 558
Caroline Series
Mathematics Institute
University of Warwick
United Kingdom