Open Sets of Maximal Dimension in Complex Hyperbolic Quasi-fuchsian Space
نویسنده
چکیده
Let π1 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 π1 into SU(2, 1), (the triple cover of) the group of holomorphic isometries of H2C. 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.
منابع مشابه
Complex hyperbolic quasi-Fuchsian groups
A complex hyperbolic quasi-Fuchsian group is a discrete, faithful, type preserving and geometrically finite representation of a surface group as a subgroup of the group of holomorphic isometries of complex hyperbolic space. Such groups are direct complex hyperbolic generalisations of quasi-Fuchsian groups in three dimensional (real) hyperbolic geometry. In this article we present the current st...
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