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Open sets of maximal dimension in complex hyperbolic quasi-Fuchsian space.

Parker, J. R. and Platis, I. D. (2006) 'Open sets of maximal dimension in complex hyperbolic quasi-Fuchsian space.', Journal of differential geometry., 73 (2). pp. 319-350.

Abstract

Let pi(1), be the fundamental group of a closed surface Sigma of genus g > 1. One of the fundamental problems in complex hyperbolic geometry is to find all discrete, faithful, geometrically finite and purely loxodromic representations of pi(1) into SU(2, 1), (the triple cover of) the group of holomorphic isometries of H-C(2). In particular, given a discrete, faithful, geometrically finite and purely loxodromic representation rho(0) of pi(1), can we find an open neighbourhood of rho(0) comprising representations with these properties. We show that this is indeed the case when rho(0) preserves a totally real Lagrangian plane.

Item Type:Article
Keywords:Ideal triangle groups, Kleinian-groups, Geometry, Representations, Flexibility, Surfaces, Moduli.
Full text:PDF - Published Version (299Kb)
Status:Peer-reviewed
Publisher Web site:http://www.intlpress.com/JDG/2006/JDG-v73.php
Publisher statement:Copyright © International Press. First published in Journal of differential geometry 73 (2) 2006, published by International Press.
Record Created:29 Feb 2008
Last Modified:22 Feb 2011 09:46

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