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ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
Coordinates for Quasi-Fuchsian Punctured Torus Space

John R Parker and Jouni Parkkonen

Geometry & Topology Monographs 1 (1998) 451–478
DOI: 10.2140/gtm.1998.1.451

arXiv: math.GT/9810199

Abstract
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We consider complex Fenchel–Nielsen coordinates on the quasi-Fuchsian space of punctured tori. These coordinates arise from a generalisation of Kra’s plumbing construction and are related to earthquakes on Teichmüller space. They also allow us to interpolate between two coordinate systems on Teichmüller space, namely the classical Fuchsian space with Fenchel–Nielsen coordinates and the Maskit embedding. We also show how they relate to the pleating coordinates of Keen and Series.

Keywords
quasi-Fuchsian space, complex Fenchel-Nielsen coordinates, pleating coordinates
Mathematical Subject Classification
Primary: 20H10
Secondary: 32G15
References
Publication
Received: 12 November 1997
Revised: 12 August 1998
Published: 27 October 1998
Authors
John R Parker
Department of Mathematical Sciences
University of Durham
Durham DH1 3LE
United Kingdom
Jouni Parkkonen
Department of Mathematics
University of Jyväskylä
P.O.Box 35
FIN-40351 Jyväskylä
Finland