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Coordinates for Quasi-Fuchsian Punctured Torus Space
John R Parker and Jouni Parkkonen
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Geometry & Topology Monographs 1
(1998) 451–478
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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.
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Keywords
quasi-Fuchsian space, complex
Fenchel-Nielsen coordinates, pleating coordinates
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Mathematical Subject Classification
Primary: 20H10
Secondary: 32G15
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Publication
Received: 12 November 1997
Revised: 12 August 1998
Published: 27 October 1998
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