Article contents
Complex length coordinates for quasi-fuchsian groups
Part of:
Riemann surfaces
Published online by Cambridge University Press: 26 February 2010
Extract
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].
MSC classification
Secondary:
30F40: Kleinian groups
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- Research Article
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- Copyright © University College London 1994
References
Ab.Abikoff, W.. The real analytic theory of Teichmüller spaces. Lecture Notes in Mathematics, (Springer-Verlag, 1980).Google Scholar
Br.Bers, L.. Spaces of Kleinian groups. In Several Complex Variables 1, 1, Maryland 1970, ed. J. Horváth, Lecture Notes in Mathematics, 155 Springer-Verlag, 1970).Google Scholar
Gd.Gardiner, F. Trace moduli for Teichmüller spaces of Kleinian groups.. J. Analyse Math., 32 (1977), 212–221.CrossRefGoogle Scholar
Gm.Goldman, W. M.. The symplectic nature of fundamental groups of surfaces. Advances in Mathematics, 54 (1984), 200–225.CrossRefGoogle Scholar
Hv.Harvey, W. J.. Spaces of discrete groups. In Discrete Groups and Automorphic Functions, ed.. Harvey, W. J. (Academic press (1977), 295–348.Google Scholar
Kn.Keen, L.. Trace moduli for quasi-Fuchsian groups. J. Math. Kyoto Univ., 26 (1986), 81–94.Google Scholar
KS.Keen, L. and Series, C.. Pleating Coordinates for the Maskit Embedding of the Teichmüller Space of Punctured Tori (Warwick preprint, 1991).Google Scholar
K1.Kourouniotis, C.. Bending in the space of quasi-Fuchsian structures. Glasgow Mathematics Journal, 33 (1991), 41–49.CrossRefGoogle Scholar
K2.Kourouniotis, C.. The geometry of bending quasi-Fuchsian groups. In Discrete groups and geometry, Papers dedicated to Macbeath, A. M., ed. and Harvey, W. J. with MacLachlan, C.. London Mathematical Society Lecture Notes Series, 173 (Cambridge University Press, (1992), 148–164.Google Scholar
Wp.Wolpert, S.. The Fenchel-Nielsen Deformation. Annals of Mathematics, 115 (1982), 501–528.CrossRefGoogle Scholar
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