Rank 1 deformations of non-cocompact hyperbolic lattices

2017/02/02 by Samuel A. Ballas, Ballas, Samuel A., Julien Paupert +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1702.00508

openalex publication_date 2017/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a negatively curved symmetric space and Γ a non-cocompact lattice in \rmIsom(X). We show that small, parabolic-preserving deformations of Γ into the isometry group of any negatively curved symmetric space containing X remain discrete and faithful (the cocompact case is due to Guichard). This applies in particular to a version of Johnson-Millson bending deformations, providing for all n infnitely many non-cocompact lattices in \rm SO(n,1) which admit discrete and faithful deformations into \rm SU(n,1). We also produce deformations of the figure-8 knot group into \rmSU(3,1), not of bending type, to which the result applies.

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