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Complex length coordinates for quasi-fuchsian groups

  • Christos Kourouniotis (a1)
  • DOI:
  • Published online: 01 February 2010

Deformation spaces of quasi-Fuchsian groups provide the simplest nontrivial examples of deformation spaces of Kleinian groups. Their understanding is of interest with respect to the study of more general Kleinian groups. On the other hand, these spaces contain subspaces isomorphic to Teichmüller spaces, and are often useful for the study of properties of Teichmüller space. A recent example of this is the study of the Teichmüller space of the punctured torus by Keen and Series [KS].

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Bd.A. F. Beardon . The Geometry of Discrete Groups (Springer-Verlag, 1983).

Br.L. Bers . Spaces of Kleinian groups. In Several Complex Variables 1, 1, Maryland 1970, ed. J. Horváth, Lecture Notes in Mathematics, 155 Springer-Verlag, 1970).

Fn.W. Fenchel . Elementary Geometry in Hyperbolic Space (de Gruyter, 1989).

Gd.F Gardiner . Trace moduli for Teichmüller spaces of Kleinian groups.. J. Analyse Math., 32 (1977), 212221.

Gm.W. M. Goldman . The symplectic nature of fundamental groups of surfaces. Advances in Mathematics, 54 (1984), 200225.

Wp.S. Wolpert . The Fenchel-Nielsen Deformation. Annals of Mathematics, 115 (1982), 501528.

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