Open Sets of Maximal Dimension in Complex Hyperbolic Quasi-Fuchsian Space

Parker, J.R.; Platis, I.D.

J. Differential Geom., Tome 72 (2006) no. 1, p. 319-350 / Harvested from Project Euclid

Résumé

Let π be the fundamental group of a closed surface Σ 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 π into SU(2, 1), (the triple cover of) the group of holomorphic isometries of H²_C. In particular, given a discrete, faithful, geometrically finite and purely loxodromic representation ρ₀ of π₁, can we find an open neighbourhood of ρ₀ comprising representations with these properties. We show that this is indeed the case when ρ₀ preserves a totally real Lagrangian plane.

Publié le : 2006-06-14
Classification:

@article{1146169913,
     author = {Parker, J.R. and Platis, I.D.},
     title = {Open Sets of Maximal Dimension in Complex Hyperbolic Quasi-Fuchsian Space},
     journal = {J. Differential Geom.},
     volume = {72},
     number = {1},
     year = {2006},
     pages = { 319-350},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1146169913}
}

Parker, J.R.; Platis, I.D. Open Sets of Maximal Dimension in Complex Hyperbolic Quasi-Fuchsian Space. J. Differential Geom., Tome 72 (2006) no. 1, pp.  319-350. http://gdmltest.u-ga.fr/item/1146169913/