Geometry & Topology Monographs 1 (1998), The Epstein Birthday Schrift, paper no. 22, pages 451-478.

Coordinates for Quasi-Fuchsian Punctured Torus Space

John R Parker, Jouni Parkkonen

Abstract. 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 Teichmueller space. They also allow us to interpolate between two coordinate systems on Teichmueller 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

AMS subject classification. Primary: 20H10. Secondary: 32G15.

E-print: arXiv:math.GT/9810199

Submitted: 12 November 1997. (Revised: 12 August 1998.) Published: 27 October 1998.

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John R Parker, Jouni Parkkonen
Department of Mathematical Sciences, University of Durham
Durham DH1 3LE, England

Department of Mathematics, University of Jyvaskyla
P.O.Box 35, FIN-40351 Jyvaskyla, Finland


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