Professor John Parker j.r.parker@durham.ac.uk
Professor
Open sets of maximal dimension in complex hyperbolic quasi-Fuchsian space
Parker, John R; Platis, Ioannis D
Authors
Ioannis D Platis
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.
Citation
Parker, J. R., & Platis, I. D. (2006). Open sets of maximal dimension in complex hyperbolic quasi-Fuchsian space. Journal of Differential Geometry, 73(2), 319-350
Journal Article Type | Article |
---|---|
Publication Date | 2006-06 |
Deposit Date | Feb 29, 2008 |
Publicly Available Date | Feb 22, 2011 |
Journal | Journal of Differential Geometry |
Print ISSN | 0022-040X |
Publisher | International Press |
Peer Reviewed | Peer Reviewed |
Volume | 73 |
Issue | 2 |
Pages | 319-350 |
Keywords | Ideal triangle groups, Kleinian-groups, Geometry, Representations, Flexibility, Surfaces, Moduli. |
Publisher URL | http://www.intlpress.com/JDG/2006/JDG-v73.php |
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Copyright Statement
Copyright © International Press.
First published in Journal of differential geometry 73 (2) 2006, published by International Press.
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