#### Volume 17, issue 4 (2013)

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Discrete primitive-stable representations with large rank surplus

### Yair N Minsky and Yoav Moriah

Geometry & Topology 17 (2013) 2223–2261
##### Abstract

We construct a sequence of primitive-stable representations of free groups into ${PSL}_{2}\left(ℂ\right)$ whose ranks go to infinity, but whose images are discrete with quotient manifolds that converge geometrically to a knot complement. In particular this implies that the rank and geometry of the image of a primitive-stable representation imposes no constraint on the rank of the domain.

##### Keywords
primitive stable, Whitehead graph, representation, rank, Dehn filling
##### Mathematical Subject Classification 2010
Primary: 57M60
Secondary: 57M50, 57M05