Some new behaviour in the deformation theory of Kleinian groups

2000/10/16 by John Holt, Holt, John
Mathematics · #57M50 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M50

paper · pdf · doi:10.48550/arxiv.math/0010164

20 pages; 2 figures. To be published in Comm. in Anal and Geom

arxiv created 2000/10/16 · arxiv updated 2009/11/30

Abstract

We present examples of hyperbolizable 3-manifolds M with the following property. Let CC(π₁(M)) denote the space of convex co-compact representations of π₁(M). We show that for every K≥ 1 there exists a representation ρ in CC(π₁(M)) so that every K-quasiconformal deformation of ρ lies in the closure of every component of CC(π₁(M)). The examples M were discovered by Anderson and Canary.

Related

• The topology of deformation spaces of Kleinian groups
• Peripheral subgroups of Kleinian groups
• Convex co-compact representations of 3-manifold groups
• Constructing geometrically infinite groups on boundaries of deformation spaces
• Strong convergence of Kleinian groups: the cracked eggshell