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

Parker, John R; Platis, Ioannis D

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

Parker, John R; Platis, Ioannis D

Authors

Professor John Parker j.r.parker@durham.ac.uk
Professor

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 © International Press.
First published in Journal of differential geometry 73 (2) 2006, published by International Press.