#### 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
##### Publication
Received: 30 September 2010
Revised: 16 October 2012
Accepted: 25 April 2013
Published: 30 July 2013
Proposed: Martin Bridson
Seconded: Danny Calegari, Benson Farb
##### Authors
 Yair N Minsky Department of Mathematics Yale University PO Box 208283 New Haven, CT 06520 USA http://www.math.yale.edu/users/yair Yoav Moriah Department of Mathematics Technion 32000 Haifa Israel http://www.math.technion.ac.il/~ymoriah/